Asymptotic Normality of Quadratic Estimators.
Robins, James; Li, Lingling; Tchetgen, Eric; van der Vaart, Aad
2016-12-01
We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data. We show that estimators are asymptotically normal even in the case that the rate is slower than the square root of the observations.
ASYMPTOTIC NORMALITY OF PARAMETERS ESTIMATION IN EV MODEL WITH REPLICATED OBSERVATIONS
Institute of Scientific and Technical Information of China (English)
张三国; 陈希孺
2002-01-01
This paper based on the essay [1], studies in case that replicated observations are available in some experimental points, the parameters estimation of one dimensional linear errors-in-variables (EV) models. Asymptotic normality is established.
GPS position time-series analysis based on asymptotic normality of M-estimation
Khodabandeh, A.; Amiri-Simkooei, A.R; Sharifi, M.A.
2011-01-01
The efficacy of robust M-estimators is a well-known issue when dealing with observational blunders. When the number of observations is considerably large—long time series for instance—one can take advantage of the asymptotic normality of the M-estimation and compute reasonable estimates for the unkn
ASYMPTOTIC NORMALITY OF QUASI MAXIMUM LIKELIHOOD ESTIMATE IN GENERALIZED LINEAR MODELS
Institute of Scientific and Technical Information of China (English)
YUE LI; CHEN XIRU
2005-01-01
For the Generalized Linear Model (GLM), under some conditions including that the specification of the expectation is correct, it is shown that the Quasi Maximum Likelihood Estimate (QMLE) of the parameter-vector is asymptotic normal. It is also shown that the asymptotic covariance matrix of the QMLE reaches its minimum (in the positive-definte sense) in case that the specification of the covariance matrix is correct.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of two estimators are proved. It is shown that the backfitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies.
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YIN; Changming; ZHAO; Lincheng; WEI; Chengdong
2006-01-01
In a generalized linear model with q × 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ∑ni=1 ZiZ'i, the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.
Directory of Open Access Journals (Sweden)
Yang Zu
2015-07-01
Full Text Available This paper studies the asymptotic normality for the kernel deconvolution estimator when the noise distribution is logarithmic chi-square; both identical and independently distributed observations and strong mixing observations are considered. The dependent case of the result is applied to obtain the pointwise asymptotic distribution of the deconvolution volatility density estimator in discrete-time stochastic volatility models.
Asymptotic Normality of LS Estimate in Simple Linear EV Regression Model
Institute of Scientific and Technical Information of China (English)
Jixue LIU
2006-01-01
Though EV model is theoretically more appropriate for applications in which measurement errors exist, people are still more inclined to use the ordinary regression models and the traditional LS method owing to the difficulties of statistical inference and computation. So it is meaningful to study the performance of LS estimate in EV model.In this article we obtain general conditions guaranteeing the asymptotic normality of the estimates of regression coefficients in the linear EV model. It is noticeable that the result is in some way different from the corresponding result in the ordinary regression model.
A New Family of Consistent and Asymptotically-Normal Estimators for the Extremal Index
Directory of Open Access Journals (Sweden)
Jose Olmo
2015-08-01
Full Text Available The extremal index (θ is the key parameter for extending extreme value theory results from i.i.d. to stationary sequences. One important property of this parameter is that its inverse determines the degree of clustering in the extremes. This article introduces a novel interpretation of the extremal index as a limiting probability characterized by two Poisson processes and a simple family of estimators derived from this new characterization. Unlike most estimators for θ in the literature, this estimator is consistent, asymptotically normal and very stable across partitions of the sample. Further, we show in an extensive simulation study that this estimator outperforms in finite samples the logs, blocks and runs estimation methods. Finally, we apply this new estimator to test for clustering of extremes in monthly time series of unemployment growth and inflation rates and conclude that runs of large unemployment rates are more prolonged than periods of high inflation.
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Qibing GAO; Yaohua WU; Chunhua ZHU; Zhanfeng WANG
2008-01-01
In generalized linear models with fixed design, under the assumption ~ →∞ and otherregularity conditions, the asymptotic normality of maximum quasi-likelihood estimator (β)n, which is the root of the quasi-likelihood equation with natural link function ∑n/i=1Xi(yi-μ(X1/iβ))=0, is obtained,where λ/-n denotes the minimum eigenvalue of ∑n/i=1XiX/1/i, Xi are bounded p x q regressors, and yi are q × 1 responses.
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TANG NianSheng; CHEN XueDong; WANG XueRen
2009-01-01
Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of two estimators are proved. It is shown that the backtitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies.
On asymptotic normality of pseudo likelihood estimates for pairwise interaction processes
DEFF Research Database (Denmark)
Jensen, Jens Ledet; Künsch, Hans R.
1994-01-01
We consider point processes defined through a pairwise interaction potential and admitting a two-dimensional sufficient statistic. It is shown that the pseudo maximum likelihood estimate can be stochastically normed so that the limiting distribution is a standard normal distribution. This result...... is true irrespectively of the possible existence of phase transitions. The work here is an extension of the work Guyon and Künsch (1992, Lecture Notes in Statist., 74, Springer, New York) and is based on viewing a point process interchangeably as a lattice field. © 1994 The Institute of Statistical...
Institute of Scientific and Technical Information of China (English)
Jinhong YOU; CHEN Min; Gemai CHEN
2004-01-01
Consider a semiparametric regression model with linear time series errors Yκ = x′κβ + g(tκ) + εκ,1 ≤ k ≤ n, where Yκ's are responses, xκ= (xκ1,xκ2,…,xκp)′and tκ ∈ T( ) R are fixed design points, β = (β1,β2,…… ,βp)′ is an unknown parameter vector, g(.) is an unknown bounded real-valued function defined on a compact subset T of the real line R, and εκ is a linear process given by εκ = ∑∞j=0 ψjeκ-j, ψ0 = 1, where ∑∞j=0 |ψj| ＜∞, and ej, j = 0,±1,±2,…, are I.I.d, random variables. In this paper we establish the asymptotic normality of the least squares estimator ofβ, a smooth estimator of g(·), and estimators of the autocovariance and autocorrelation functions of the linear process εκ.
ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE
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林正炎
2003-01-01
Let {Xn,n> _ 1} be a strictly stationary sequence of random variables,which are either associated or negatively associated,f(·)be their common density.In this paper,the author shows a central limit theorem for a kernel estimate of f(·)under certain regular conditions.
Local asymptotic normality and asymptotical minimax efficiency of the MLE under random censorship
Institute of Scientific and Technical Information of China (English)
王启华; 荆炳义
2000-01-01
Here we study the problems of local asymptotic normality of the parametric family of distri-butions and asymptotic minimax efficient estimators when the observations are subject to right censor-ing. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and fur-thermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient.
Local asymptotic normality and asymptotical minimax efficiency of the MLE under random censorship
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Here we study the problems of local asymptotic normality of the parametric family of distributions and asymptotic minimax efficient estimators when the observations are subject to right censoring. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and furthermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient.
ASYMPTOTICS OF MEAN TRANSFORMATION ESTIMATORS WITH ERRORS IN VARIABLES MODEL
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CUI Hengjian
2005-01-01
This paper addresses estimation and its asymptotics of mean transformation θ = E[h(X)] of a random variable X based on n iid. Observations from errors-in-variables model Y = X + v, where v is a measurement error with a known distribution and h(.) is a known smooth function. The asymptotics of deconvolution kernel estimator for ordinary smooth error distribution and expectation extrapolation estimator are given for normal error distribution respectively. Under some mild regularity conditions, the consistency and asymptotically normality are obtained for both type of estimators. Simulations show they have good performance.
Asymptotics for Kernel Estimation of Slicing Average Third-Moment Estimation
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Li-ping Zhu; Li-xing Zhu
2006-01-01
To estimate central dimension-reduction space in multivariate nonparametric regression, Sliced Inverse Regression[7] (SIR), Sliced Average Variance Estimation[4] (SAVE) and Slicing Average Third-moment Estimation[14] (SAT) have been developed. Since slicing estimation has very different asymptotic behavior for SIR and SAVE, the relevant study has been made case by case, when the kernel estimators of SIR and SAVE share similar asymptotic properties. In this paper, we also investigate kernel estimation of SAT. We prove the asymptotic normality, and show that, compared with the existing results, the kernel smoothing for SIR, SAVE and SAT has very similar asymptotic behavior.
A Shortcut to LAD Estimator Asymptotics
1990-01-01
Using generalized functions of random variables and generalized Taylor series expansions, we provide almost trivial demonstrations of the asymptotic theory for the LAD estimator in a regression model setting. The approach is justified by the smoothing that is delivered in the limit by the asymptotics, whereby the generalized functions are forced to appear as linear functionals wherein they become real valued. Models with fixed and random regressors, autoregressions and autoregressions with in...
ON ASYMPTOTIC NORMALITY OF PARAMETERS IN MULTIPLE LINEAR ERRORS-IN-VARIABLES MODEL
Institute of Scientific and Technical Information of China (English)
ZHANG Sanguo; CHEN Xiru
2003-01-01
This paper studies the parameter estimation of multiple dimensional linear errors-in-variables (EV) models in the case where replicated observations are available in some experimental points. Asymptotic normality is established under mild conditions, and the parameters entering the asymptotic variance are consistently estimated to render the result useable in the construction of large-sample confidence regions.
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孙婷; 凌能祥
2015-01-01
In this paper ,the asymptotic property of modified kernel regression estimation for functional stationary ergodic data is researched w hen the explanatory variable X has functional characteristic and the response variable Y is a scalar in real‐value space R .Specifically ,the modified kernel estimation of the regression function r(x) is constructed by using the classic Nadaraya‐Watson estimator .Under certain conditions ,the asymptotic normality of modified kernel regression estimation for functional stationary ergodic data is established by applying the martingale difference central limit theorem , which extends the α‐mixing data to the functional stationary ergodic data .%文章基于解释变量 X具有函数特征而响应变量Y 取值于实数空间R的条件下，研究了基于平稳遍历函数型数据改良核回归估计的渐近性质。利用经典的N‐W核估计的方法构造了回归函数 r（x）的改良核估计，在一定的条件下，应用鞅差中心极限定理建立了基于平稳遍历函数型数据改良核回归估计的渐近正态性，从而推广了现有文献中的相关结果。
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施红星
2012-01-01
考虑响应变量随机缺失下线性模型响应变量均值的估计问题，分别获得了基于完全观测样本数据、线性回归插补后的“完全样本”和逆概率加权插补后的“完全样本”得到的响应变量均值估计，并证明了其渐近正态性．%The present study considers the linear models with response variable data missing at random and investigates the estimation of the mean of response variables, from which we have obtained asymptotic normality of estimators based on the completely observed pairs, the ＇complete＇ data after linear regression imputation and the ＇complete＇ data after inverse probability weighted imputation.
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Jie Li DING; Xi Ru CHEN
2006-01-01
For generalized linear models (GLM), in case the regressors are stochastic and have different distributions, the asymptotic properties of the maximum likelihood estimate (MLE)(β^)n of the parameters are studied. Under reasonable conditions, we prove the weak, strong consistency and asymptotic normality of(β^)n.
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夏天; 孔繁超
2008-01-01
本文我们提出了一些正则条件,这些条件减弱了Zhu and Wei(1997)文的条件.基于所提的正则条件,我们证明了指数族非线性模型参数最大似然估计的相合性和渐近正态性.我们的结果可被认为是Zhu and Wei(1997)工作的进一步改进.%This paper proposes some regularity conditions which weaken those given by Zhu & Wei (1997).On the basis of the proposed regularity conditions,the existence,the strong consistency and the asymptotic normality of maximum likelihood estimation(MLE)are proved in exponential family nonlinear models(EFNMs).Our results may be regarded as a further improvement of the work of Zhu & Wei(1997).
Asymptotic variance of grey-scale surface area estimators
DEFF Research Database (Denmark)
Svane, Anne Marie
Grey-scale local algorithms have been suggested as a fast way of estimating surface area from grey-scale digital images. Their asymptotic mean has already been described. In this paper, the asymptotic behaviour of the variance is studied in isotropic and sufficiently smooth settings, resulting...... in a general asymptotic bound. For compact convex sets with nowhere vanishing Gaussian curvature, the asymptotics can be described more explicitly. As in the case of volume estimators, the variance is decomposed into a lattice sum and an oscillating term of at most the same magnitude....
Error estimates in horocycle averages asymptotics: challenges from string theory
Cardella, M.A.
2010-01-01
For modular functions of rapid decay, a classical result connects the error estimate in their long horocycle average asymptotic to the Riemann hypothesis. We study similar asymptotics, for modular functions with not that mild growing conditions, such as of polynomial growth and of exponential growth
Asymptotic estimates for generalized Stirling numbers
Chelluri, R.; Richmond, L.B.; Temme, N.M.
1999-01-01
Uniform asymptotic expansions are given for the Stirling numbers of the first kind for integral arguments and for the second kind as defined for real arguments by Flajolet and Prodinger. The logconcavity of the resulting real valued function of Flajolet and Prodinger is established for a range inclu
Estimating exercise stroke volume from asymptotic oxygen pulse in humans.
Whipp, B J; Higgenbotham, M B; Cobb, F C
1996-12-01
Noninvasive techniques have been devised to estimate cardiac output (Q) during exercise to obviate vascular cannulation. However, although these techniques are noninvasive, they are commonly not nonintrusive to subjects' spontaneous ventilation and gas-exchange responses. We hypothesized that the exercise stroke volume (SV) and, hence, Q might be accurately estimated simply from the response pattern of two standardly determined variables: O2 uptake (VO2) and heart rate (HR). Central to the theory is the demonstration that the product of Q and mixed venous O2 content is virtually constant (k) during steady-state exercise. Thus from the Fick equation, VO2 = Q.CaCO2-k, where CaCO2 is the arterial CO2 content, the O2 pulse (O2-P) equals SV.CaCO2-(k/HR). Because the arterial O2 content (CaO2) is usually relatively constant in normal subjects during exercise, O2-P should change hyperbolically with HR, asymptoting at SV.CaO2. In addition, because the asymptotic O2-P equals the slope (S) of the linear O2-HR relationship, exercise SV may be predicted as S/CaO2. We tested this prediction in 23 normal subjects who underwent a 3-min incremental cycle-ergometer test with direct determination of CaO2 and mixed venous O2 content from indwelling catheters. The predicted SV closely reflected the measured value (r = 0.80). We therefore conclude that, in normal subjects, exercise SV may be estimated simply as five times S of the linear VO2-HR relationship (where 5 is approximately 1/CaO2).
Radius of 9C from the Asymptotic Normalization Coefficient
Institute of Scientific and Technical Information of China (English)
LI Zhi-Hong; GUO Bing; LIU Wei-Ping; BAI Xi-Xiang; LIAN Gang; SU Jun; YAN Sheng-Quan; WANG Bao-Xiang; ZENG Sheng
2005-01-01
@@ The asymptotic normalization coefficient (ANC) of9 C = 8 B+p deduced from 8 Li(d, p)9 Li reaction is used to obtainthe root-mean-square (rms) radius of the loosely bound proton in the 9C ground state. We obtain 1/2 = 3.61 fmfor the valence proton, which is significantly larger than the matter radius of 9 C. The probability of the valence proton outside the matter radius of 9 C is greater than 60%. The present work supports the conclusion that 9 Chas a proton halo structure.
Asymptotic normality of recursive algorithms via martingale difference arrays
Directory of Open Access Journals (Sweden)
Werner Schachinger
2001-12-01
Full Text Available We propose martingale central limit theorems as an tool to prove asymptotic normality of the costs of certain recursive algorithms which are subjected to random input data. The recursive algorithms that we have in mind are such that if input data of size N produce random costs L N, then L N = D L n + L N-n +R N for N ≥ n 0 ≥2, where n follows a certain distribution P N on the integers {0, … ,N} and L k = D L k for k≥0. L n, L N-n and R N are independent, conditional on n, and R N are random variables, which may also depend on n, corresponding to the cost of splitting the input data of size N (into subsets of size n and N-n and combining the results of the recursive calls to yield the overall result. We construct a martingale difference array with rows converging to Z N:= [L N- EL N ] / [√ Var L N ]. Under certain compatibility assumptions on the sequence (P N N≥0 we show that a pair of sufficient conditions (of Lyapunov type for Z N → D N(0,1 can be restated as a pair of conditions regarding asymptotic relations between three sequences. All these sequences satisfy the same type of linear equation, that is also the defining equation for the sequence (EL N N≥0 and thus very likely a well studied object. In the case that the P N are binomial distributions with the same parameter p, and for deterministic R N, we demonstrate the power of this approach. We derive very general sufficient conditions in terms of the sequence (R N N≥0 (and for the scale R N =N α a characterization of those α leading to asymptotic normality of Z N.
DEFF Research Database (Denmark)
Ørregård Nielsen, Morten
2015-01-01
This article proves consistency and asymptotic normality for the conditional-sum-of-squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time-series models. The model is parametric and quite general and, in particular, encompasses...
DEFF Research Database (Denmark)
Ørregård Nielsen, Morten
This paper proves consistency and asymptotic normality for the conditional-sum-of-squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time series models. The model is parametric and quite general, and, in particular, encompasses...
Fisher information and asymptotic normality in system identification for quantum Markov chains
Guta, Madalin
2010-01-01
This paper deals with the problem of estimating the coupling constant $\\theta$ of a mixing quantum Markov chain with finite dimensional quantum systems. For a repeated measurement on the chain's output we show that the outcomes' time average has an asymptotically normal (Gaussian) distribution, and we give the explicit expressions of its mean and variance. This provides a simple estimator of $\\theta$ with computable classical Fisher information which can be optimized over different choices of measurements. We then show that the output itself is asymptotically normal, i.e. at time $n$ the joint output states with parameters of the form $\\theta_{0}+u/\\sqrt{n}$ look like a one dimensional family of coherent states with displacement $u\\sqrt{F/2}$, where $F$ is the quantum Fisher information of the output. These results are quantum extensions of theorems from the theory of classical Markov chains, and further extensions to continuous time dynamics and multiple parameters are in preparation.
Asymptotic Distribution of the Jump Change-Point Estimator
Institute of Scientific and Technical Information of China (English)
Changchun TAN; Huifang NIU; Baiqi MIAO
2012-01-01
The asymptotic distribution of the change-point estimator in a jump changepoint model is considered.For the jump change-point model Xi =a + θI{[nTo] ＜ i ≤n} + εi,where εi (i =1,…,n) are independent identically distributed random variables with Eεi=0 and Var(εi) ＜ oo,with the help of the slip window method,the asymptotic distribution of the jump change-point estimator (T) is studied under the condition of the local alternative hypothesis.
Asymptotic stability estimates near an equilibrium point
Dumas, H. Scott; Meyer, Kenneth R.; Palacián, Jesús F.; Yanguas, Patricia
2017-07-01
We use the error bounds for adiabatic invariants found in the work of Chartier, Murua and Sanz-Serna [3] to bound the solutions of a Hamiltonian system near an equilibrium over exponentially long times. Our estimates depend only on the linearized system and not on the higher order terms as in KAM theory, nor do we require any steepness or convexity conditions as in Nekhoroshev theory. We require that the equilibrium point where our estimate applies satisfy a type of formal stability called Lie stability.
Estimation and asymptotic inference in the first order AR-ARCH model
DEFF Research Database (Denmark)
Lange, Theis; Rahbek, Anders; Jensen, Søren Tolver
2011-01-01
This article studies asymptotic properties of the quasi-maximum likelihood estimator (QMLE) for the parameters in the autoregressive (AR) model with autoregressive conditional heteroskedastic (ARCH) errors. A modified QMLE (MQMLE) is also studied. This estimator is based on truncation of individual...... terms of the likelihood function and is related to the recent so-called self-weighted QMLE in Ling (2007b). We show that the MQMLE is asymptotically normal irrespectively of the existence of finite moments, as geometric ergodicity alone suffice. Moreover, our included simulations show that the MQMLE...... for the QMLE to be asymptotically normal. Finally, geometric ergodicity for AR-ARCH processes is shown to hold under mild and classic conditions on the AR and ARCH processes....
Sinharay, Sandip
2015-01-01
The maximum likelihood estimate (MLE) of the ability parameter of an item response theory model with known item parameters was proved to be asymptotically normally distributed under a set of regularity conditions for tests involving dichotomous items and a unidimensional ability parameter (Klauer, 1990; Lord, 1983). This article first considers…
DEFF Research Database (Denmark)
Hubalek, Friedrich; Posedel, Petra
We provide a simple explicit estimator for discretely observed Barndorff-Nielsen and Shephard models, prove rigorously consistency and asymptotic normality based on the single assumption that all moments of the stationary distribution of the variance process are finite, and give explicit expressi...
Asymptotic accuracy of Bayesian estimation for a single latent variable.
Yamazaki, Keisuke
2015-09-01
In data science and machine learning, hierarchical parametric models, such as mixture models, are often used. They contain two kinds of variables: observable variables, which represent the parts of the data that can be directly measured, and latent variables, which represent the underlying processes that generate the data. Although there has been an increase in research on the estimation accuracy for observable variables, the theoretical analysis of estimating latent variables has not been thoroughly investigated. In a previous study, we determined the accuracy of a Bayes estimation for the joint probability of the latent variables in a dataset, and we proved that the Bayes method is asymptotically more accurate than the maximum-likelihood method. However, the accuracy of the Bayes estimation for a single latent variable remains unknown. In the present paper, we derive the asymptotic expansions of the error functions, which are defined by the Kullback-Leibler divergence, for two types of single-variable estimations when the statistical regularity is satisfied. Our results indicate that the accuracies of the Bayes and maximum-likelihood methods are asymptotically equivalent and clarify that the Bayes method is only advantageous for multivariable estimations.
Asymptotic normality of the QMLE in the level-effect ARCH model
DEFF Research Database (Denmark)
Dahl, Christian Møller; Iglesias, Emma M.
In this paper consistency and asymptotic normality of the quasi maximum like-lihood estimator in the level-effect ARCH model of Chan, Karolyi, Longstaff and Sanders (1992) is established. We consider explicitly the case where the parameters of the conditional heteroskedastic process...... are in the stationary region and discuss carefully how the results can be extended to the region where the conditional heteroskedastic process is nonstationary. The results illustrate that Jensen and Rahbek's (2004a,2004b) approach can be extended further than to traditional ARCH and GARCH models....
Asymptotic Properties of Spectral Estimates of Second-Order with Missed Observations
Directory of Open Access Journals (Sweden)
G. S. Mokaddis
2010-01-01
Full Text Available Problem statement: As a complement of the periodogram study the asymptotic properties of the spectral density using data window for stationary stochastic process are investigated. Some statistical properties of covariance estimation function with missing observations are studied. Approach: The asymptotic normality was discussed. A numerical example was discussed by using computer programming. Results: The study of time series with missed observations and with the modified periodogram had the same results of the study of the classic time series. Conclusion: Modified periodogram with expanded finite Fourier transformation for time series with missed observation has improved the results of the classic time series.
Asymptotic normality of the size of the giant component in a random hypergraph
Bollobas, Bela
2011-01-01
Recently, we adapted random walk arguments based on work of Nachmias and Peres, Martin-L\\"of, Karp and Aldous to give a simple proof of the asymptotic normality of the size of the giant component in the random graph $G(n,p)$ above the phase transition. Here we show that the same method applies to the analogous model of random $k$-uniform hypergraphs, establishing asymptotic normality throughout the (sparse) supercritical regime. Previously, asymptotic normality was known only towards the two ends of this regime.
Precise Asymptotics of Error Variance Estimator in Partially Linear Models
Institute of Scientific and Technical Information of China (English)
Shao-jun Guo; Min Chen; Feng Liu
2008-01-01
In this paper, we focus our attention on the precise asymptoties of error variance estimator in partially linear regression models, yi = xTi β + g(ti) +εi, 1 ≤i≤n, {εi,i = 1,... ,n } are i.i.d random errors with mean 0 and positive finite variance q2. Following the ideas of Allan Gut and Aurel Spataru[7,8] and Zhang[21],on precise asymptotics in the Baum-Katz and Davis laws of large numbers and precise rate in laws of the iterated logarithm, respectively, and subject to some regular conditions, we obtain the corresponding results in partially linear regression models.
On Estimating the Parameters of Truncated Trivariate Normal Distributions
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M. N. Bhattacharyya
1969-07-01
Full Text Available Maximum likehood estimates of the parameters of a trivariate normal distribution, with single truncation on two-variates, have been derived in this paper. The information matrix has also been given from which the asymptotic variances and covariances might be obtained for the estimates of the parameters of the restricted variables. Numerical examples have been worked out.
Asymptotic theory of nonparametric regression estimates with censored data
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
For regression analysis, some useful information may have been lost when the responses are right censored. To estimate nonparametric functions, several estimates based on censored data have been proposed and their consistency and convergence rates have been studied in literature, but the optimal rates of global convergence have not been obtained yet. Because of the possible information loss, one may think that it is impossible for an estimate based on censored data to achieve the optimal rates of global convergence for nonparametric regression, which were established by Stone based on complete data. This paper constructs a regression spline estimate of a general nonparametric regression function based on right_censored response data, and proves, under some regularity conditions, that this estimate achieves the optimal rates of global convergence for nonparametric regression. Since the parameters for the nonparametric regression estimate have to be chosen based on a data driven criterion, we also obtain the asymptotic optimality of AIC, AICC, GCV, Cp and FPE criteria in the process of selecting the parameters.
ESTIMATION FOR THE ASYMPTOTIC BEHAVIOR OF THE DELAYED COMPETITION MODEL
Institute of Scientific and Technical Information of China (English)
Li Huifeng; Wang Jinliang
2008-01-01
In ecological dynamic systems, the competition between species is a very universal phenomenon, which can be described by the well-known Volterra-Lotka model in a diffusion form. Noticing that the living space usually changes in a seasonal manner and the population development of the species may also undergo time-delay im-pact, a developed form of this model is investigated in this article. The main approaches employed here are the upper-lower solution method and the energy-estimate technique. The results show that whether the species may sustain survival or not depends on the relations among the birth rate, the death rate, the competition rate, the diffusivity and the time delay. For the survival case, the population evolutions of the two species may appear asymptotic periodicity with distinct upper bound and this bound depends heavily on the time delay. These results can be also checked by the intuitionistic numerical simulations.
Cruz, Pedro
2011-01-01
It is shown the almost sure convergence and asymptotical normality of a generalization of Kesten's stochastic approximation algorithm for multidimensional case. In this generalization, the step increases or decreases if the scalar product of two subsequente increments of the estimates is positive or negative. This rule is intended to accelerate the entrance in the `stochastic behaviour' when initial conditions cause the algorithm to behave in a `deterministic fashion' for the starting iterations.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The generalized linear model(GLM) based on the observed data with incomplete information in the case of random censorship is defined. Under the given conditions, the existence and uniqueness of the solution on the likelihood equations with respect to the parameter vector β of the model are discussed, and the consistency and asymptotic normality of the maximum likelihood estimator(MLE) ^βn are proved.
Czabarka, Eva; Johnson, Virginia; Kupczok, Anne; Szekely, Laszlo A
2011-01-01
P.L. Erdos and L.A. Szekely [Adv. Appl. Math. 10(1989), 488-496] gave a bijection between rooted semilabeled trees and set partitions. L.H. Harper's results [Ann. Math. Stat. 38(1967), 410-414] on the asymptotic normality of the Stirling numbers of the second kind translates into asymptotic normality of rooted semilabeled trees with given number of vertices, when the number of internal vertices varies. The Erdos-Szekely bijection specializes to a bijection between phylogenetic trees and set partitions with classes of size \\geq 2. We consider modified Stirling numbers of the second kind that enumerate partitions of a fixed set into a given number of classes of size \\geq 2, and obtain their asymptotic normality as the number of classes varies. The Erdos- Szekely bijection translates this result into the asymptotic normality of the number of phylogenetic trees with given number of vertices, when the number of leaves varies. We also obtain asymptotic normality of the number of phylogenetic trees with given number...
Asymptotics of Huber-Dutter Estimators for Partial Linear Model with Nonstochastic Designs
Institute of Scientific and Technical Information of China (English)
Xing-wei Tong; Heng-jian Cui; Hui Zhao
2005-01-01
For partial linear model Y = Xτ0 + g0(T) + e with unknown β0 ∈ Rd and an unknown smooth function go, this paper considers the Huber-Dutter estimators ofβ0, scale σ for the errors and the function go respectively, in which the smoothing B-spline function is used. Under some regular conditions, it is shown that the Huber-Dutter estimators of β0 and σ are asymptotically normal with convergence rate n-1/2 and the B-spline Huber-Dutter estimator of g0 achieves the optimal convergence rate in nonparametric regression.A simulation study demonstrates that the Huber-Dutter estimator ofβ0 is competitive with its M-estimator without scale parameter and the ordinary least square estimator. An example is presented after the simulation study.
Uniform Asymptotic Normality of the Matrix-variate Beta-distribution
Institute of Scientific and Technical Information of China (English)
Kai Can LI; He TANG
2012-01-01
With the upper bound of Kullback-Leibler distance between a matrix variate Beta-distribution and a normal distribution,this paper gives the conditions under which a matrix-variate Betadistribution will approach uniformly and asymptotically a normal distribution.
ASYMPTOTIC EXPANSION AND ESTIMATE OF THE LANDAU CONSTANT
Institute of Scientific and Technical Information of China (English)
A.Eisinberg; G.Franzè; N.Salerno
2001-01-01
Properties of Landau constant are investigated in this note.A new representation in terms of a hypergeometric function 3F2 is given and a property defining the family of asymptotic sequences of Landau constant is formalized.Moreover,we give an other asymptotic expansion of Landau constant by using asymptotic expansion of the ratio of gamma functions in the sense of Poincaré due to Tricomi and Erdélyi.
Asymptotics of Bonferroni for Dependent Normal Test Statistics.
Proschan, Michael A; Shaw, Pamela A
2011-07-01
The Bonferroni adjustment is sometimes used to control the familywise error rate (FWE) when the number of comparisons is huge. In genome wide association studies, researchers compare cases to controls with respect to thousands of single nucleotide polymorphisms. It has been claimed that the Bonferroni adjustment is only slightly conservative if the comparisons are nearly independent. We show that the veracity of this claim depends on how one defines "nearly." Specifically, if the test statistics' pairwise correlations converge to 0 as the number of tests tend to ∞, the conservatism of the Bonferroni procedure depends on their rate of convergence. The type I error rate of Bonferroni can tend to 0 or 1 - exp(-α) ≈ α, depending on that rate. We show using elementary probability theory what happens to the distribution of the number of errors when using Bonferroni, as the number of dependent normal test statistics gets large. We also use the limiting behavior of Bonferroni to shed light on properties of other commonly used test statistics.
The Asymptotic Posterior Normality of the Latent Trait for Polytomous IRT Models.
Chang, Hua-Hua
1996-01-01
H. H. Chang and W. F. Stout (1993) presented a derivation of the asymptotic posterior normality of the latent trait given examinee responses under nonrestrictive nonparametric assumptions for dichotomous item response (IRT) theory models. This paper presents an extension of their results to polytomous IRT models and defines a global information…
The asymptotic distribution of a cluster-index for i.i.d. normal random variables
Yatracos, Yannis G.
2009-01-01
In a sample variance decomposition, with components functions of the sample's spacings, the largest component $\\tilde{I}_n$ is used in cluster detection. It is shown for normal samples that the asymptotic distribution of $\\tilde{I}_n$ is the Gumbel distribution.
State Estimation for a Biological Phosphorus Removal Process using an Asymptotic Observer
DEFF Research Database (Denmark)
Larose, Claude Alain; Jørgensen, Sten Bay
2001-01-01
This study investigated the use of an asymptotic observer for state estimation in a continuous biological phosphorus removal process. The estimated states are the concentration of heterotrophic, autotrophic, and phosphorus accumulating organisms, polyphosphate, glycogen and PHA. The reaction scheme...
The Asymptotic Standard Errors of Some Estimates of Uncertainty in the Two-Way Contingency Table
Brown, Morton B.
1975-01-01
Estimates of conditional uncertainty, contingent uncertainty, and normed modifications of contingent uncertainity have been proposed for the two-way contingency table. The asymptotic standard errors of the estimates are derived. (Author)
M-Estimation for Discrete Data. Asymptotic Distribution Theory and Implications.
1985-10-01
DATA: ASYMPTOTIC DISTRIBUTION THEORY AND IMPLICATIONS by 1 Douglas G. Simpson Departr.ient of Statistics University of Illinois Urbana, Illinois...asymptotic distribution theory of M-estimators especially relevant to discrete data, although Theorem 1 is somewhat broader in scope’. The main results are...The version (2.5) c (X9 / - ), where s(a)=9 / + (c) is defined by (2.3), is slightly more convenient. 3. Extended asymptotic distribution theory Conditions
Asymptotic Parameter Estimation for a Class of Linear Stochastic Systems Using Kalman-Bucy Filtering
Directory of Open Access Journals (Sweden)
Xiu Kan
2012-01-01
Full Text Available The asymptotic parameter estimation is investigated for a class of linear stochastic systems with unknown parameter θ:dXt=(θα(t+β(tXtdt+σ(tdWt. Continuous-time Kalman-Bucy linear filtering theory is first used to estimate the unknown parameter θ based on Bayesian analysis. Then, some sufficient conditions on coefficients are given to analyze the asymptotic convergence of the estimator. Finally, the strong consistent property of the estimator is discussed by comparison theorem.
Invariant Measures and Asymptotic Gaussian Bounds for Normal Forms of Stochastic Climate Model
Institute of Scientific and Technical Information of China (English)
Yuan YUAN; Andrew J.MAJDA
2011-01-01
The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive high dimensional climate models is an important topic for atmospheric low-frequency variability, climate sensitivity, and improved extended range forecasting. Recently, techniques from applied mathematics have been utilized to systematically derive normal forms for reduced stochastic climate models for low-frequency variables. It was shown that dyad and multiplicative triad interactions combine with the climatological linear operator interactions to produce a normal form with both strong nonlinear cubic dissipation and Correlated Additive and Multiplicative (CAM) stochastic noise. The probability distribution functions (PDFs) of low frequency climate variables exhibit small but significant departure from Gaussianity but have asymptotic tails which decay at most like a Gaussian. Here, rigorous upper bounds with Gaussian decay are proved for the invariant measure of general normal form stochastic models. Asymptotic Gaussian lower bounds are also established under suitable hypotheses.
The estimation-valued property of B-valued asymptotic martingale
Institute of Scientific and Technical Information of China (English)
KONG Fanliang
2006-01-01
In this paper, with the Doob decomposition of B-valued asymptotic martingale, we study the estimation-valued property of B-valued asymptotic martingale in Banach space B, which has the Radon-Nikodym Property and is dual-separable, and give a series of result and proof.
M-Estimation for Discrete Data: Asymptotic Distribution Theory and Implications.
1985-11-01
n 860 0029 M-ESTIMATION FOR DISCRETE DATA: ASYMPTOTIC DISTRIBUTION THEORY AND IMPLICATIONS by Douglas G. Simpson 1 Departraent of Statistics... distribution theory of M-estimators especially relevant to discrete data, although Theorem 1 is somewhat broader in scope’. The main results are given in...Extended asymptotic distribution theory Conditions for consistency of an M-estimator can be found in Huber (1964, 1967, 1981). Since the smoothness plays
Heo, Jun-Haeng; Boes, D. C.; Salas, J. D.
2001-02-01
Parameter estimation in a regional flood frequency setting, based on a Weibull model, is revisited. A two parameter Weibull distribution at each site, with common shape parameter over sites that is rationalized by a flood index assumption, and with independence in space and time, is assumed. The estimation techniques of method of moments and method of probability weighted moments are studied by proposing a family of estimators for each technique and deriving the asymptotic variance of each estimator. Then a single estimator and its asymptotic variance for each technique, suggested by trying to minimize the asymptotic variance over the family of estimators, is obtained. These asymptotic variances are compared to the Cramer-Rao Lower Bound, which is known to be the asymptotic variance of the maximum likelihood estimator. A companion paper considers the application of this model and these estimation techniques to a real data set. It includes a simulation study designed to indicate the sample size required for compatibility of the asymptotic results to fixed sample sizes.
On asymptotically optimal wavelet estimation of trend functions under long-range dependence
Beran, Jan; 10.3150/10-BEJ332
2012-01-01
We consider data-adaptive wavelet estimation of a trend function in a time series model with strongly dependent Gaussian residuals. Asymptotic expressions for the optimal mean integrated squared error and corresponding optimal smoothing and resolution parameters are derived. Due to adaptation to the properties of the underlying trend function, the approach shows very good performance for smooth trend functions while remaining competitive with minimax wavelet estimation for functions with discontinuities. Simulations illustrate the asymptotic results and finite-sample behavior.
Institute of Scientific and Technical Information of China (English)
武新乾; 田铮; 句彦伟
2006-01-01
Consider the model Yt = βYt-1 + g(Yt-2) + εt for 3 ≤ t ≤ T . Here g is an unknown function,β is an unknown parameter, εt are i.i.d. random errors with mean 0 and variance σ2 and the fourth moment c4, and εt are independent of Ys for all t ≥ 3 and s = 1,2.Pseudo-LS estimators (σ)2T, (α)4T and (D)2T of σ2, α4 and Var(ε23) are respectively constructed based on piecewise polynomial approximator of g. The weak consistency of (α)4T and (D)2T are proved. The asymptotic normality of (α)2T is given, i.e., (√T)((σ)2T- σ2)/(D)T converges in distribution to N(0,1). The result can be used to establish large sample interval estimates of σ2 or to make large sample tests for σ2.
Sharp asymptotic estimates for vorticity solutions of the 2D Navier-Stokes equation
Directory of Open Access Journals (Sweden)
Yuncheng You
2008-12-01
Full Text Available The asymptotic dynamics of high-order temporal-spatial derivatives of the two-dimensional vorticity and velocity of an incompressible, viscous fluid flow in $mathbb{R}^2$ are studied, which is equivalent to the 2D Navier-Stokes equation. It is known that for any integrable initial vorticity, the 2D vorticity solution converges to the Oseen vortex. In this paper, sharp exterior decay estimates of the temporal-spatial derivatives of the vorticity solution are established. These estimates are then used and combined with similarity and $L^p$ compactness to show the asymptotical attraction rates of temporal-spatial derivatives of generic 2D vorticity and velocity solutions by the Oseen vortices and velocity solutions respectively. The asymptotic estimates and the asymptotic attraction rates of all the derivatives obtained in this paper are independent of low or high Reynolds numbers.
Langer, S F J; Habazettl, H; Kuebler, W M; Pries, A R
2005-01-01
The left ventricular isovolumic pressure decay, obtained by cardiac catheterization, is widely characterized by the time constant tau of the exponential regression p(t)=Pomega+(P0-Pomega)exp(-t/tau). However, several authors prefer to prefix Pomega=0 instead of coestimating the pressure asymptote empirically; others present tau values estimated by both methods that often lead to discordant results and interpretation of lusitropic changes. The present study aims to clarify the relations between the tau estimates from both methods and to decide for the more reliable estimate. The effect of presetting a zero asymptote on the tau estimate was investigated mathematically and empirically, based on left ventricular pressure decay data from isolated ejecting rat and guinea pig hearts at different preload and during spontaneous decrease of cardiac function. Estimating tau with preset Pomega=0 always yields smaller values than the regression with empirically estimated asymptote if the latter is negative and vice versa. The sequences of tau estimates from both methods can therefore proceed in reverse direction if tau and Pomega change in opposite directions between the measurements. This is exemplified by data obtained during an increasing preload in spontaneously depressed isolated hearts. The estimation of the time constant of isovolumic pressure fall with a preset zero asymptote is heavily biased and cannot be used for comparing the lusitropic state of the heart in hemodynamic conditions with considerably altered pressure asymptotes.
Indirect Techniques in Nuclear Astrophysics. Asymptotic Normalization Coefficient and Trojan Horse
Energy Technology Data Exchange (ETDEWEB)
Mukhamedzhanov, A.M. [Cyclotron Institute, Texas A and M University, College Station, TX, 77843 (United States); Blokhintsev, L.D. [Institute of Nuclear Physics, Moscow State University, Moscow (Russian Federation); Brown, S. [Florida State University, Tallahassee, FL (United States)] (and others)
2007-05-01
We address two important indirect techniques, the asymptotic normalization coefficient (ANC) and the Trojan Horse (TH) methods. We discuss the application of the ANC technique to determine the astrophysical factor for the {sup 13}C({alpha}, n){sup 16}O reaction which is one of the neutron generators for the s processes in AGB stars. The TH method is a unique indirect technique allowing one to measure astrophysical S factors for rearrangement reactions down to astrophysically relevant energies. We derive equations connecting the cross sections for the binary direct and resonant reactions determined from the indirect TH reactions to direct cross sections measurements.
State Estimation for a Biological Phosphorus Removal Process using an Asymptotic Observer
DEFF Research Database (Denmark)
Larose, Claude Alain; Jørgensen, Sten Bay
2001-01-01
This study investigated the use of an asymptotic observer for state estimation in a continuous biological phosphorus removal process. The estimated states are the concentration of heterotrophic, autotrophic, and phosphorus accumulating organisms, polyphosphate, glycogen and PHA. The reaction scheme...... if the convergence, driven by the dilution rate, was slow (from 15 to 60 days). The propagation of the measurement noise and a bias in the estimation of glycogen and PHA could be the result of the high condition number of one of the matrices used in the algorithm of the asymptotic observer for the aerated tanks....
An asymptotically unbiased minimum density power divergence estimator for the Pareto-tail index
DEFF Research Database (Denmark)
Dierckx, Goedele; Goegebeur, Yuri; Guillou, Armelle
2013-01-01
We introduce a robust and asymptotically unbiased estimator for the tail index of Pareto-type distributions. The estimator is obtained by fitting the extended Pareto distribution to the relative excesses over a high threshold with the minimum density power divergence criterion. Consistency...
An asymptotically unbiased minimum density power divergence estimator for the Pareto-tail index
DEFF Research Database (Denmark)
Dierckx, G.; Goegebeur, Y.; Guillou, A.
2013-01-01
We introduce a robust and asymptotically unbiased estimator for the tail index of Pareto-type distributions. The estimator is obtained by fitting the extended Pareto distribution to the relative excesses over a high threshold with the minimum density power divergence criterion. Consistency and as...... by a small simulation experiment involving both uncontaminated and contaminated samples. (C) 2013 Elsevier Inc. All rights reserved....
Asymptotic theory of nonparametric regression estimates with censored data
Institute of Scientific and Technical Information of China (English)
施沛德; 王海燕; 张利华
2000-01-01
For regression analysis, some useful Information may have been lost when the responses are right censored. To estimate nonparametric functions, several estimates based on censored data have been proposed and their consistency and convergence rates have been studied in literat黵e, but the optimal rates of global convergence have not been obtained yet. Because of the possible Information loss, one may think that it is impossible for an estimate based on censored data to achieve the optimal rates of global convergence for nonparametric regression, which were established by Stone based on complete data. This paper constructs a regression spline estimate of a general nonparametric regression f unction based on right-censored response data, and proves, under some regularity condi-tions, that this estimate achieves the optimal rates of global convergence for nonparametric regression. Since the parameters for the nonparametric regression estimate have to be chosen based on a data driven criterion, we also obtai
Maximal admissible faces and asymptotic bounds for the normal surface solution space
Burton, Benjamin A
2010-01-01
The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dimensional polytope, where admissibility is a powerful but non-linear and non-convex constraint. The main results of this paper are significant improvements upon the best known asymptotic bounds on the number of admissible vertices, using polytopes in both the standard normal surface coordinate system and the streamlined quadrilateral coordinate system. To achieve these results we examine the layout of admissible points within these polytopes. We show that these points correspond to well-behaved substructures of the face lattice, and we study properties of the corresponding "admissible faces". Key lemmata include upper bounds on the number of maximal admissible faces of each dimension, and a bijection between the maximal admissible faces in the two coordinate systems mentioned above.
Improved Estimators of the Mean of a Normal Distribution with a Known Coefficient of Variation
Directory of Open Access Journals (Sweden)
Wuttichai Srisodaphol
2012-01-01
Full Text Available This paper is to find the estimators of the mean θ for a normal distribution with mean θ and variance aθ2, a>0, θ>0. These estimators are proposed when the coefficient of variation is known. A mean square error (MSE is a criterion to evaluate the estimators. The results show that the proposed estimators have preference for asymptotic comparisons. Moreover, the estimator based on jackknife technique has preference over others proposed estimators with some simulations studies.
ASYMPTOTIC EFFICIENT ESTIMATION IN SEMIPARAMETRIC NONLINEAR REGRESSION MODELS
Institute of Scientific and Technical Information of China (English)
ZhuZhongyi; WeiBocheng
1999-01-01
In this paper, the estimation method based on the “generalized profile likelihood” for the conditionally parametric models in the paper given by Severini and Wong (1992) is extendedto fixed design semiparametrie nonlinear regression models. For these semiparametrie nonlinear regression models,the resulting estimator of parametric component of the model is shown to beasymptotically efficient and the strong convergence rate of nonparametric component is investigated. Many results (for example Chen (1988) ,Gao & Zhao (1993), Rice (1986) et al. ) are extended to fixed design semiparametric nonlinear regression models.
Asymptotic Normalization Coefficient of 27P→26Si+p and Radius of 27P Halo
Institute of Scientific and Technical Information of China (English)
GUO Bing; LI Zhi-Hong; LIU Wei-Ping; BAI Xi-Xiang
2006-01-01
The asymptotic normalization coefficient of the virtual decay 27P→26Si+p is extracted to be 1840±240 fm-1 from the peripheral 26Mg(d,p)27Mg reaction using charge symmetry of mirror pair,for the first time.It is then used to derive the rms radius of the valence proton in the ground state of 27P.We obtain the rms radius 1/2=4.57±0.36 fm,significantly larger than the matter radius of 27P.The probability of the valence proton outside the matter radius of 27P is found to be 73%.The present work supports the conclusion that the 27P ground state has a proton halo structure.
Indirect techniques in nuclear astrophysics. Asymptotic Normalization Coefficient and Trojan Horse
Mukhamedzhanov, A M; Brown, B A; Burjan, V; Cherubini, S; Gagliardi, C A; Irgaziev, B F; Kroha, V; Nunes, F M; Pirlepesov, F; Pizzone, R G; Romano, S; Spitaleri, C; Tang, X D; Trache, L; Tribble, R E; Tumino, A
2005-01-01
Owing to the presence of the Coulomb barrier at astrophysically relevant kinetic energies it is very difficult, or sometimes impossible, to measure astrophysical reaction rates in the laboratory. That is why different indirect techniques are being used along with direct measurements. Here we address two important indirect techniques, the asymptotic normalization coefficient (ANC) and the Trojan Horse (TH) methods. We discuss the application of the ANC technique for calculation of the astrophysical processes in the presence of subthreshold bound states, in particular, two different mechanisms are discussed: direct capture to the subthreshold state and capture to the low-lying bound states through the subthreshold state, which plays the role of the subthreshold resonance. The ANC technique can also be used to determine the interference sign of the resonant and nonresonant (direct) terms of the reaction amplitude. The TH method is unique indirect technique allowing one to measure astrophysical rearrangement reac...
Zollanvari, Amin
2013-05-24
We provide a fundamental theorem that can be used in conjunction with Kolmogorov asymptotic conditions to derive the first moments of well-known estimators of the actual error rate in linear discriminant analysis of a multivariate Gaussian model under the assumption of a common known covariance matrix. The estimators studied in this paper are plug-in and smoothed resubstitution error estimators, both of which have not been studied before under Kolmogorov asymptotic conditions. As a result of this work, we present an optimal smoothing parameter that makes the smoothed resubstitution an unbiased estimator of the true error. For the sake of completeness, we further show how to utilize the presented fundamental theorem to achieve several previously reported results, namely the first moment of the resubstitution estimator and the actual error rate. We provide numerical examples to show the accuracy of the succeeding finite sample approximations in situations where the number of dimensions is comparable or even larger than the sample size.
Zollanvari, Amin; Genton, Marc G
2013-08-01
We provide a fundamental theorem that can be used in conjunction with Kolmogorov asymptotic conditions to derive the first moments of well-known estimators of the actual error rate in linear discriminant analysis of a multivariate Gaussian model under the assumption of a common known covariance matrix. The estimators studied in this paper are plug-in and smoothed resubstitution error estimators, both of which have not been studied before under Kolmogorov asymptotic conditions. As a result of this work, we present an optimal smoothing parameter that makes the smoothed resubstitution an unbiased estimator of the true error. For the sake of completeness, we further show how to utilize the presented fundamental theorem to achieve several previously reported results, namely the first moment of the resubstitution estimator and the actual error rate. We provide numerical examples to show the accuracy of the succeeding finite sample approximations in situations where the number of dimensions is comparable or even larger than the sample size.
Timmerman, Marieke E.; Kiers, Henk A.L.; Smilde, Age K.
2007-01-01
Confidence intervals (Cis) in principal component analysis (PCA) can be based on asymptotic standard errors and on the bootstrap methodology. The present paper offers an overview of possible strategies for bootstrapping in PCA. A motivating example shows that Ci estimates for the component loadings
Consistency Estimations and Asymptotical Properties in AHP with Multi-deciders
Institute of Scientific and Technical Information of China (English)
ZHAO Ji-chao; ZHANG Zhi-min
2002-01-01
In this paper, we define two types of synthetic comparison matrices by using geometrical average and arithmetical average, it is shown that there exist consistency estimations and asymptotical properties of synthetic comparison matrices and its perturbation matrices in AHP with multi-deciders. The Hadamard decomposition of the synthetic comparison matrix defined by geometrical average is also given.
Error estimates for asymptotic solutions of dynamic equations on time scales
Directory of Open Access Journals (Sweden)
Gro Hovhannisyan
2007-02-01
Full Text Available We establish error estimates for first-order linear systems of equations and linear second-order dynamic equations on time scales by using calculus on a time scales [1,4,5] and Birkhoff-Levinson's method of asymptotic solutions [3,6,8,9].
Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials
Navas, Luis M; Varona, Juan L
2011-01-01
We analyze the asymptotic behavior of the Apostol-Bernoulli polynomials $\\mathcal{B}_{n}(x;\\lambda)$ in detail. The starting point is their Fourier series on $[0,1]$ which, it is shown, remains valid as an asymptotic expansion over compact subsets of the complex plane. This is used to determine explicit estimates on the constants in the approximation, and also to analyze oscillatory phenomena which arise in certain cases. These results are transferred to the Apostol-Euler polynomials $\\mathcal{E}_{n}(x;\\lambda)$ via a simple relation linking them to the Apostol-Bernoulli polynomials.
Some asymptotic results on density estimators by wavelet projections
Varron, Davit
2012-01-01
Let $(X_i)_{i\\geq 1}$ be an i.i.d. sample on $\\RRR^d$ having density $f$. Given a real function $\\phi$ on $\\RRR^d$ with finite variation and given an integer valued sequence $(j_n)$, let $\\fn$ denote the estimator of $f$ by wavelet projection based on $\\phi$ and with multiresolution level equal to $j_n$. We provide exact rates of almost sure convergence to 0 of the quantity $\\sup_{x\\in H}\\mid \\fn(x)-\\EEE(\\fn)(x)\\mid$, when $n2^{-dj_n}/\\log n \\rar \\infty$ and $H$ is a given hypercube of $\\RRR^d$. We then show that, if $n2^{-dj_n}/\\log n \\rar c$ for a constant $c>0$, then the quantity $\\sup_{x\\in H}\\mid \\fn(x)-f\\mid$ almost surely fails to converge to 0.
Asymptotic properties of maximum likelihood estimators in models with multiple change points
He, Heping; 10.3150/09-BEJ232
2011-01-01
Models with multiple change points are used in many fields; however, the theoretical properties of maximum likelihood estimators of such models have received relatively little attention. The goal of this paper is to establish the asymptotic properties of maximum likelihood estimators of the parameters of a multiple change-point model for a general class of models in which the form of the distribution can change from segment to segment and in which, possibly, there are parameters that are common to all segments. Consistency of the maximum likelihood estimators of the change points is established and the rate of convergence is determined; the asymptotic distribution of the maximum likelihood estimators of the parameters of the within-segment distributions is also derived. Since the approach used in single change-point models is not easily extended to multiple change-point models, these results require the introduction of those tools for analyzing the likelihood function in a multiple change-point model.
Indirect techniques in nuclear astrophysics. Asymptotic normalization coefficient and trojan horse
Energy Technology Data Exchange (ETDEWEB)
Mukhamedzhanov, A.M.; Gagliardi, C.A.; Pirlepesov, F.; Trache, L.; Tribble, R.E. [Texas A and M University, Cyclotron Institute, College Station, TX (United States); Blokhintsev, L.D. [Moscow State University, Institute of Nuclear Physics, Moscow (Russian Federation); Brown, B.A.; Nunes, F.M. [Michigan State University, N.S.C.L. and Department of Physics and Astronomy, East Lansing, MI (United States); Burjan, V.; Kroha, V. [Nuclear Physics Institute of Czech Academy of Sciences, Prague-Rez (Czech Republic); Cherubini, S.; Pizzone, R.G.; Romano, S.; Spitaleri, C.; Tumino, A. [DMFCI, Universita di Catania, Catania, Italy and INFN, Laboratori Nazionali del Sud, Catania (Italy); Irgaziev, B.F. [National University, Physics Department, Tashkent (Uzbekistan); Tang, X.D. [Argonne National Laboratory, Physics Division, Argonne, IL (United States)
2006-03-15
Owing to the presence of the Coulomb barrier at astrophysically relevant kinetic energies it is very difficult, or sometimes impossible, to measure astrophysical reaction rates in the laboratory. That is why different indirect techniques are being used along with direct measurements. Here we address two important indirect techniques, the asymptotic normalization coefficient (ANC) and the Trojan Horse (TH) methods. We discuss the application of the ANC technique for calculation of the astrophysical processes in the presence of subthreshold bound states, in particular, two different mechanisms are discussed: direct capture to the subthreshold state and capture to the low-lying bound states through the subthreshold state, which plays the role of the subthreshold resonance. The ANC technique can also be used to determine the interference sign of the resonant and nonresonant (direct) terms of the reaction amplitude. The TH method is unique indirect technique allowing one to measure astrophysical rearrangement reactions down to astrophysically relevant energies. We explain why there is no Coulomb barrier in the sub-process amplitudes extracted from the TH reaction. The expressions for the TH amplitude for direct and resonant cases are presented. (orig.)
The choice of the ability estimate with asymptotically correct standardized person-fit statistics.
Sinharay, Sandip
2016-05-01
Snijders (2001, Psychometrika, 66, 331) suggested a statistical adjustment to obtain the asymptotically correct standardized versions of a specific class of person-fit statistics. His adjustment has been used to obtain the asymptotically correct standardized versions of several person-fit statistics including the lz statistic (Drasgow et al., 1985, Br. J. Math. Stat. Psychol., 38, 67), the infit and outfit statistics (e.g., Wright & Masters, 1982, Rating scale analysis, Chicago, IL: Mesa Press), and the standardized extended caution indices (Tatsuoka, 1984, Psychometrika, 49, 95). Snijders (2001), van Krimpen-Stoop and Meijer (1999, Appl. Psychol. Meas., 23, 327), Magis et al. (2012, J. Educ. Behav. Stat., 37, 57), Magis et al. (2014, J. Appl. Meas., 15, 82), and Sinharay (2015b, Psychometrika, doi:10.1007/s11336-015-9465-x, 2016b, Corrections of standardized extended caution indices, Unpublished manuscript) have used the maximum likelihood estimate, the weighted likelihood estimate, and the posterior mode of the examinee ability with the adjustment of Snijders (2001). This paper broadens the applicability of the adjustment of Snijders (2001) by showing how other ability estimates such as the expected a posteriori estimate, the biweight estimate (Mislevy & Bock, 1982, Educ. Psychol. Meas., 42, 725), and the Huber estimate (Schuster & Yuan, 2011, J. Educ. Behav. Stat., 36, 720) can be used with the adjustment. A simulation study is performed to examine the Type I error rate and power of two asymptotically correct standardized person-fit statistics with several ability estimates. A real data illustration follows.
An Asymptotic Normal Procedure With Censorship%终检渐近正态法
Institute of Scientific and Technical Information of China (English)
赵长华; 杨兵
2015-01-01
目的：：基于经典渐近正态法，提出一种用于两生存率检验所需样本量的测定的终检渐近正态法。方法：该方法是终检样本的实际样本量随终检概率和时间衰减形成的有效样本量。结果：它具有还原性，摆脱了指数分布的假设，与两生存率检验相匹配；其观测功效和预定功效吻合；相比之下，终检非中心法略显保守， Lachin-Foulkes法对于生存率检验显得功效不足。结论：这种方法适于慢性病临床研究，以检出早、中、晚期疗效差别。%Objective An asymptotic normal procedure with censorship is proposed for determining the sample size required in the test on two survival rates. Methods The procedure is derived from its classical counterpart on the basis of that the real size of censored samples declines with the censoring probability and the time. Results It is re-ducible, free from the assumption of exponential distributions, and matched with the test on two survival rates. The observed power coincides with the prescribed power. By contrast, the non -central procedure with censorship is slightly conservative and the Lachin-Foulkes procedure has the power usually not adequate for the test on two sur-vival rates. Conclusion The procedure is appropriate with planning clinical studies of chronic diseases for detecting early, middle, or late treatment-control difference.
Shin, Hyun Kyung; Choi, Bongsik; Talkner, Peter; Lee, Eok Kyun
2014-12-07
Based on the generalized Langevin equation for the momentum of a Brownian particle a generalized asymptotic Einstein relation is derived. It agrees with the well-known Einstein relation in the case of normal diffusion but continues to hold for sub- and super-diffusive spreading of the Brownian particle's mean square displacement. The generalized asymptotic Einstein relation is used to analyze data obtained from molecular dynamics simulations of a two-dimensional soft disk fluid. We mainly concentrated on medium densities for which we found super-diffusive behavior of a tagged fluid particle. At higher densities a range of normal diffusion can be identified. The motion presumably changes to sub-diffusion for even higher densities.
Fleury, R. M. N.; Hills, D. A.; Ramesh, R.; Barber, J. R.
2017-02-01
We develop a method for the solution of partial slip contact problems suffering complex loading cycles where, generally, the normal load, shear force and, potentially, differential bulk tensions are all functions of time, using an edge-asymptote approach. The size of the slip zone and local shear traction distribution are revealed as functions of time. The results are then re-worked in asymptotic form, so that they do not hinge on inherent symmetry and anti-symmetry conditions for the contact overall, and are of general applicability. The multipliers on the local solutions (generalised stress intensity factors) are also appropriate as a means of taking laboratory tests quantifying fretting fatigue and employing them to wholly different prototypical problems.
2012-01-01
We show the analytic continuation of the resolvent of the Laplacian on asymptotically hyperbolic spaces on differential forms, including high energy estimates in strips. This is achieved by placing the spectral family of the Laplacian within the framework developed, and applied to scalar problems, by the author recently, roughly by extending the problem across the boundary of the compactification of the asymptotically hyperbolic space in a suitable manner. The main novelty is that the non-sca...
Bibinger, Markus
2011-01-01
The article is devoted to the nonparametric estimation of the quadratic covariation of non-synchronously observed It\\^o processes in an additive microstructure noise model. In a high-frequency setting, we aim at establishing an asymptotic distribution theory for a generalized multiscale estimator including a feasible central limit theorem with optimal convergence rate on convenient regularity assumptions. The inevitably remaining impact of asynchronous deterministic sampling schemes and noise corruption on the asymptotic distribution is precisely elucidated. A case study for various important examples, several generalizations of the model and an algorithm for the implementation warrant the utility of the estimation method in applications.
Design of asymptotic estimators: an approach based on neural networks and nonlinear programming.
Alessandri, Angelo; Cervellera, Cristiano; Sanguineti, Marcello
2007-01-01
A methodology to design state estimators for a class of nonlinear continuous-time dynamic systems that is based on neural networks and nonlinear programming is proposed. The estimator has the structure of a Luenberger observer with a linear gain and a parameterized (in general, nonlinear) function, whose argument is an innovation term representing the difference between the current measurement and its prediction. The problem of the estimator design consists in finding the values of the gain and of the parameters that guarantee the asymptotic stability of the estimation error. Toward this end, if a neural network is used to take on this function, the parameters (i.e., the neural weights) are chosen, together with the gain, by constraining the derivative of a quadratic Lyapunov function for the estimation error to be negative definite on a given compact set. It is proved that it is sufficient to impose the negative definiteness of such a derivative only on a suitably dense grid of sampling points. The gain is determined by solving a Lyapunov equation. The neural weights are searched for via nonlinear programming by minimizing a cost penalizing grid-point constraints that are not satisfied. Techniques based on low-discrepancy sequences are applied to deal with a small number of sampling points, and, hence, to reduce the computational burden required to optimize the parameters. Numerical results are reported and comparisons with those obtained by the extended Kalman filter are made.
Asymptotic normality of the size of the giant component via a random walk
Bollobas, Bela
2010-01-01
In this paper we give a simple new proof of a result of Pittel and Wormald concerning the asymptotic value and (suitably rescaled) limiting distribution of the number of vertices in the giant component of $G(n,p)$ above the scaling window of the phase transition. Nachmias and Peres used martingale arguments to study Karp's exploration process, obtaining a simple proof of a weak form of this result. Here we use slightly different martingale arguments to obtain the full result of Pittel and Wormald with little extra work.
Institute of Scientific and Technical Information of China (English)
SUN Liuquan; ZHENG Zhongguo
1999-01-01
A central limit theorem for the integrated square error (ISE)of the kernel hazard rate estimators is obtained based on left truncated and right censored data.An asymptotic representation of the mean integrated square error(MISE) for the kernel hazard rate estimators is also presented.
An application of the asymptotic theory to a threshold model for the estimate of Martens Hardness
Directory of Open Access Journals (Sweden)
Grazia Vicario
2007-10-01
Full Text Available Hardness measurements have a significant role in mechanical metrology, as they are frequently used to characterise materials properties relevant to industrial processes. A recently introduced method, called Martens Hardness, is based on force and indentation records obtained during a test cycle; the Force/Depth Curve, which describes the indetation pattern, is typically formed by two parts having a zero-point in common. A segmented regression model is proposed in this paper, based on the introduction of a threshold parameter in order to estimate the unknown zero-point. The problem is not trivial, since the relationship between observed force and indentation depth is structural and, moreover, the number of nuisance parameters grows with the number of measured data. The asymptotic likelihood theory leads to an estimate of the unknown parameters of the model. Monte Carlo simulations are resorted to in order to analyse the properties of estimators under different hypotheses about measurement errors, and to etablish the applicability conditions of the method proposed.
ASYMPTOTIC ESTIMATION FOR SOLUTION OF A CLASS OF SEMI-LINEAR ROBIN PROBLEMS
Institute of Scientific and Technical Information of China (English)
Cheng Ouyang
2005-01-01
A class of semi-linear Robin problem is considered. Under appropriate assumptions, the existence and asymptotic behavior of its solution are studied more carefully. Using stretched variables, the formal asymptotic expansion of solution for the problem is constructed and the uniform validity of the solution is obtained by using the method of upper and lower solution.
Directory of Open Access Journals (Sweden)
Belyaeva T. L.
2014-03-01
Full Text Available We have performed coupled reaction channels calculations of the (d,p reactions on 12C and 10Be at laboratory energies of 12, 25, and 30 MeV leading to the ground and first excited states of 13C and 11Be. We found spectroscopic factors Sexp, asymptotic normalization coefficients (ANCs and root mean square radii of the last neutron in these states. Our calculations confirm the existence of neutron halos in the first excited state of 13C, as well as in the ground and the first excited states of 11Be. We found that the neutron transfer dominates at energies about 12 and 25 MeV and demonstrated that the states with enlarged radii are formed in the reactions of a peripheral type, which satisfy the criterion of a peripherality: C2=Sexpb2=const, where C is the ANC and b is the single-particle ANC.
Estimation of sheath potentials in front of ASDEX upgrade ICRF antenna with SSWICH asymptotic code
Křivská, A.; Bobkov, V.; Colas, L.; Jacquot, J.; Milanesio, D.; Ochoukov, R.
2015-12-01
Multi-megawatt Ion Cyclotron Range of Frequencies (ICRF) heating became problematic in ASDEX Upgrade (AUG) tokamak after coating of ICRF antenna limiters and other plasma facing components by tungsten. Strong impurity influx was indeed produced at levels of injected power markedly lower than in the previous experiments. It is assumed that the impurity production is mainly driven by parallel component of Radio-Frequency (RF) antenna electric near-field E// that is rectified in sheaths. In this contribution we estimate poloidal distribution of sheath Direct Current (DC) potential in front of the ICRF antenna and simulate its relative variations over the parametric scans performed during experiments, trying to reproduce some of the experimental observations. In addition, relative comparison between two types of AUG ICRF antenna configurations, used for experiments in 2014, has been performed. For this purpose we use the Torino Polytechnic Ion Cyclotron Antenna (TOPICA) code and asymptotic version of the Self-consistent Sheaths and Waves for Ion Cyclotron Heating (SSWICH) code. Further, we investigate correlation between amplitudes of the calculated oscillating sheath voltages and the E// fields computed at the lateral side of the antenna box, in relation with a heuristic antenna design strategy at IPP Garching to mitigate RF sheaths.
Asymptotic scaling properties and estimation of the generalized Hurst exponents in financial data
Buonocore, R. J.; Aste, T.; Di Matteo, T.
2017-04-01
We propose a method to measure the Hurst exponents of financial time series. The scaling of the absolute moments against the aggregation horizon of real financial processes and of both uniscaling and multiscaling synthetic processes converges asymptotically towards linearity in log-log scale. In light of this we found appropriate a modification of the usual scaling equation via the introduction of a filter function. We devised a measurement procedure which takes into account the presence of the filter function without the need of directly estimating it. We verified that the method is unbiased within the errors by applying it to synthetic time series with known scaling properties. Finally we show an application to empirical financial time series where we fit the measured scaling exponents via a second or a fourth degree polynomial, which, because of theoretical constraints, have respectively only one and two degrees of freedom. We found that on our data set there is not clear preference between the second or fourth degree polynomial. Moreover the study of the filter functions of each time series shows common patterns of convergence depending on the momentum degree.
Estimation of sheath potentials in front of ASDEX upgrade ICRF antenna with SSWICH asymptotic code
Energy Technology Data Exchange (ETDEWEB)
Křivská, A., E-mail: alena.krivska@rma.ac.be [LPP-ERM/KMS, Royal Military Academy, 30 Avenue de la Renaissance B-1000, Brussels (Belgium); Bobkov, V.; Jacquot, J.; Ochoukov, R. [Max-Planck-Institut für Plasmaphysik, D-85748 Garching (Germany); Colas, L. [CEA, IRFM, F-13108 Saint-Paul-Lez-Durance (France); Milanesio, D. [Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino (Italy)
2015-12-10
Multi-megawatt Ion Cyclotron Range of Frequencies (ICRF) heating became problematic in ASDEX Upgrade (AUG) tokamak after coating of ICRF antenna limiters and other plasma facing components by tungsten. Strong impurity influx was indeed produced at levels of injected power markedly lower than in the previous experiments. It is assumed that the impurity production is mainly driven by parallel component of Radio-Frequency (RF) antenna electric near-field E// that is rectified in sheaths. In this contribution we estimate poloidal distribution of sheath Direct Current (DC) potential in front of the ICRF antenna and simulate its relative variations over the parametric scans performed during experiments, trying to reproduce some of the experimental observations. In addition, relative comparison between two types of AUG ICRF antenna configurations, used for experiments in 2014, has been performed. For this purpose we use the Torino Polytechnic Ion Cyclotron Antenna (TOPICA) code and asymptotic version of the Self-consistent Sheaths and Waves for Ion Cyclotron Heating (SSWICH) code. Further, we investigate correlation between amplitudes of the calculated oscillating sheath voltages and the E// fields computed at the lateral side of the antenna box, in relation with a heuristic antenna design strategy at IPP Garching to mitigate RF sheaths.
Weak Uniform Normal Structure and Fixed Points of Asymptotically Regular Semigroups
Institute of Scientific and Technical Information of China (English)
Lu Chuan ZENG
2004-01-01
Let X be a Banach space with a weak uniform normal structure and C a non-empty convexweakly compact subset of X. Under some suitable restriction, we prove that every asymptoticallyregular semigroup T = {T(t): t ∈ S} of selfmappings on C satisfyinglim inf |‖T(t)‖| ＜ WCS(X)S(∈)t→∞has a common fixed point, where WCS(X) is the weakly convergent sequence coefficient of X, and |‖T(t) ‖ | is the exact Lipschitz constant of T(t).
Consistency and normality of Huber-Dutter estimators for partial linear model
Institute of Scientific and Technical Information of China (English)
2008-01-01
For partial linear model Y = Xτβ0 + g0(T) + with unknown β0 ∈ Rd and an unknown smooth function g0, this paper considers the Huber-Dutter estimators of β0, scale σ for the errors and the function g0 approximated by the smoothing B-spline functions, respectively. Under some regularity conditions, the Huber-Dutter estimators of β0 and σ are shown to be asymptotically normal with the rate of convergence n-1/2 and the B-spline Huber-Dutter estimator of g0 achieves the optimal rate of convergence in nonparametric regression. A simulation study and two examples demonstrate that the Huber-Dutter estimator of β0 is competitive with its M-estimator without scale parameter and the ordinary least square estimator.
Consistency and normality of Huber-Dutter estimators for partial linear model
Institute of Scientific and Technical Information of China (English)
TONG XingWei; CUI HengJian; YU Peng
2008-01-01
For partial linear model Y = Xτβ0 + g0(T) + ∈ with unknown/β0 ∈ Rd and an unknown smooth function g0,this paper considers the Huber-Dutter estimators of/β0,scale σ for the errors and the function g0 approximated by the smoothing B-spline functions,respectively.Under some regularity conditions,the Huber-Dutter estimators of/β0 and σ are shown to be asymptotically normal with the rate of convergence n-1/2 and the B-spline Huber-Dutter estimator of go achieves the optimal rate of convergence in nonparametric regression.A simulation study and two examples demonstrate that the Huber-Dutter estimator of/β0 is competitive with its M-estimator without scale parameter and the ordinary least square estimator.
Institute of Scientific and Technical Information of China (English)
GUO Bing; LI Zhi-Hong
2007-01-01
@@ The angular distribution of the 13C(d,p)14C reaction is reanalysed using the Johnson-Soper approach. The squared asymptotic normalization coefficient (ANC) of virtual decay 14C → 13C + n is then derived to be 21.4 ±5.0 fm-1.
Institute of Scientific and Technical Information of China (English)
GUO Bing; LI Zhi-Hong; LIU Wei-Ping; BAI Xi-Xiang
2007-01-01
The asymptotic normalization coefficients (ANCs) for the virtual decay 17O→16O+n are derived from the angular distributions of the 16O(d, p)17O reaction leading to the ground and first excited states of 17O, respectively, using the distorted wave Born approximation and the adiabatic wave approximation. The ANCs of 17F are then extracted according to charge symmetry of mirror nuclei and used to calculate the astrophysical S-factors of 16O(p,γ)17F leading to the first two states of 17F. The present results are in good agreement with those from the direct measurement. This provides a test of this indirect method to determine direct astrophysical S-factors of(p, γ) reaction. In addition, the S-factors at zero energy for the direct captures to the ground and first excited states of 17F are presented, without the uncertainty associated with the extrapolation from higher energies in direct measurement.
Robust methods and asymptotic theory in nonlinear econometrics
Bierens, Herman J
1981-01-01
This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...
Institute of Scientific and Technical Information of China (English)
王德辉
2007-01-01
This paper is concerned with the distributional properties of a median unbiased estimator of ARCH(0,1) coefficient. The exact distribution of the estimator can be easily derived, however its practical calculations are too heavy to implement,even though the middle range of sample sizes. Since the estimator is shown to have asymptotic normality, asymptotic expansions for the distribution and the percentiles of the estimator are derived as the refinements. Accuracies of expansion formulas are evaluated numerically, and the results of which show that we can effectively use the expansion as a fine approximatioh of the distribution with rapid calculations. Derived expansion are applied to testing hypothesis of stationarity, and an implementation for a real data set is illustrated.
Asymptotic distributions in the projection pursuit based canonical correlation analysis
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper, associations between two sets of random variables based on the projection pursuit (PP) method are studied. The asymptotic normal distributions of estimators of the PP based canonical correlations and weighting vectors are derived.
Asymptotic admissibility of priors and elliptic differential equations
Hartigan, J A
2010-01-01
We evaluate priors by the second order asymptotic behavior of the corresponding estimators.Under certain regularity conditions, the risk differences between efficient estimators of parameters taking values in a domain D, an open connected subset of R^d, are asymptotically expressed as elliptic differential forms depending on the asymptotic covariance matrix V. Each efficient estimator has the same asymptotic risk as a 'local Bayes' estimate corresponding to a prior density p. The asymptotic decision theory of the estimators identifies the smooth prior densities as admissible or inadmissible, according to the existence of solutions to certain elliptic differential equations. The prior p is admissible if the quantity pV is sufficiently small near the boundary of D. We exhibit the unique admissible invariant prior for V=I,D=R^d-{0). A detailed example is given for a normal mixture model.
Dobbs, David E.
2010-01-01
This note develops and implements the theory of polynomial asymptotes to (graphs of) rational functions, as a generalization of the classical topics of horizontal asymptotes and oblique/slant asymptotes. Applications are given to hyperbolic asymptotes. Prerequisites include the division algorithm for polynomials with coefficients in the field of…
On asymptotics of t-type regression estimation in multiple linear model
Institute of Scientific and Technical Information of China (English)
无
2004-01-01
We consider a robust estimator (t-type regression estimator) of multiple linear regression model by maximizing marginal likelihood of a scaled t-type error t-distribution.The marginal likelihood can also be applied to the de-correlated response when the withinsubject correlation can be consistently estimated from an initial estimate of the model based on the independent working assumption. This paper shows that such a t-type estimator is consistent.
Energy Technology Data Exchange (ETDEWEB)
Igamov, S.B. [Institute of Nuclear Physics, Uzbekistan Academy of Sciences, 702132 Tashkent (Uzbekistan); Yarmukhamedov, R. [Institute of Nuclear Physics, Uzbekistan Academy of Sciences, 702132 Tashkent (Uzbekistan)]. E-mail: rakhim@inp.uz
2007-01-01
A modified two-body potential approach is proposed for determination of both the asymptotic normalization coefficient (ANC) (or the respective nuclear vertex constant (NVC)) for the A+a->B (for the virtual decay B->A+a) from an analysis of the experimental S-factor for the peripheral direct capture a+A->B+{gamma} reaction and the astrophysical S-factor, S(E), at low experimentally inaccessible energy regions. The approach proposed involves two additional conditions which verify the peripheral character of the considered reaction and expresses S(E) in terms of the ANC. The connection between NVC (ANC) and the effective range parameters for Aa-scattering is derived. To test this approach we reanalyse the precise experimental astrophysical S-factors for t+{alpha}->Li7+{gamma} reaction at energies E=<1200 keV [C.R. Brune et al., Phys. Rev. C 50 (1994) 2205]. The same Wood-Saxon potential form both for the bound (t+{alpha})-state wave function and for the {alpha}t-scattering wave function is used to guarantee selfconsistency. New estimates have been obtained for the values of the ANC's (the NVC's) for the {alpha}+t->Li7(g.s.), {alpha}+t->Li7(0.478 MeV) and of S(E) at E=<50 keV. These ANC values have been used for getting information about the ''indirect'' measured values of the effective range parameters and the p-wave phase shift for {alpha}t-scattering in the energy range of 100-bar E-bar 180 keV.
Estimation of CN Parameter for Small Agricultural Watersheds Using Asymptotic Functions
Directory of Open Access Journals (Sweden)
Tomasz Kowalik
2015-03-01
Full Text Available This paper investigates a possibility of using asymptotic functions to determine the value of curve number (CN parameter as a function of rainfall in small agricultural watersheds. It also compares the actually calculated CN with its values provided in the Soil Conservation Service (SCS National Engineering Handbook Section 4: Hydrology (NEH-4 and Technical Release 20 (TR-20. The analysis showed that empirical CN values presented in the National Engineering Handbook tables differed from the actually observed values. Calculations revealed a strong correlation between the observed CN and precipitation (P. In three of the analyzed watersheds, a typical pattern of the observed CN stabilization during abundant precipitation was perceived. It was found that Model 2, based on a kinetics equation, most effectively described the P-CN relationship. In most cases, the observed CN in the investigated watersheds was similar to the empirical CN, corresponding to average moisture conditions set out by NEH-4. Model 2 also provided the greatest stability of CN at 90% sampled event rainfall.
Estimation and asymptotic theory for transition probabilities in Markov Renewal Multi–state models
Spitoni, C.; Verduijn, M.; Putter, H.
2012-01-01
In this paper we discuss estimation of transition probabilities for semi–Markov multi–state models. Non–parametric and semi–parametric estimators of the transition probabilities for a large class of models (forward going models) are proposed. Large sample theory is derived using the functional delta
On the Asymptotic Distribution of Signal Fraction
Volobouev, Igor
2016-01-01
Condition of the asymptotic normality of the signal fraction estimate by maximum likelihood is derived under the null hypothesis of no signal. Consequences of this condition for determination of signal significance taking in to account the look elsewhere effect are discussed.
Asymptotic estimation theory of multipoint linkage analysis under perfect marker information
Hössjer, Ola
2003-01-01
We consider estimation of a disease susceptibility locus $\\tau$ at a chromosome. With perfect marker data available, the estimator $\\htau_N$ of $\\tau$ based on $N$-pedigrees has a rate of convergence $N^{-1}$ under mild regularity conditions. The limiting distribution is the arg max of a certain compound Poisson process. Our approach is conditional on observed phenotypes, and therefore treats parametric and nonparametric linkage, as well as quantitative trait loci methods within a unified fra...
Institute of Scientific and Technical Information of China (English)
WU Kai-Su; CHEN Yong-Shou; LIU Zu-Hua; LIN Cheng-Jian; ZHANG Huan-Qiao
2003-01-01
The cross section of the direct neutron capture reaction 12C(n,7)13C(l/2+) is calculated with the asymptotic normalization coefficient method. The result is in good agreement with a recent experiment at low energy. An enormous enhancement of cross section is found for this direct neutron capture in which a p-wave neutron is captured into an 2?i/2 orbit with neutron halo. The possible effect of the neutron halo structure presented in this reaction on the s-process in astrophysics is discussed in general.
De Marco, Stefano
2011-01-01
We study smoothness of densities for the solutions of SDEs whose coefficients are smooth and nondegenerate only on an open domain $D$. We prove that a smooth density exists on $D$ and give upper bounds for this density. Under some additional conditions (mainly dealing with the growth of the coefficients and their derivatives), we formulate upper bounds that are suitable to obtain asymptotic estimates of the density for large values of the state variable ("tail" estimates). These results specify and extend some results by Kusuoka and Stroock [J. Fac. Sci. Univ. Tokyo Sect. IA Math. 32 (1985) 1--76], but our approach is substantially different and based on a technique to estimate the Fourier transform inspired from Fournier [Electron. J. Probab. 13 (2008) 135--156] and Bally [Integration by parts formula for locally smooth laws and applications to equations with jumps I (2007) The Royal Swedish Academy of Sciences]. This study is motivated by existing models for financial securities which rely on SDEs with non-...
LOCAL ASYMPTOTIC PROPERTIES OF HAZARD RATE ESTIMATORS FOR TRUNCATED AND CENSORED DATA
Institute of Scientific and Technical Information of China (English)
SUN Liuquan; WU Guofu; WEI Xianhua
2001-01-01
Functional laws of the iterated logarithm are obtained for cumulative hazard processes in the neighborhood of a fixed point when the data are subject to left truncation and right censorship. On the basis of these results the exact rates of pointwise almost sure convergence for various types of kernel hazard rate estimators are derived.
Skakala, Jozef
2011-01-01
We analyze the largely accepted formulas for the asymptotic quasi-normal frequencies of the non-extremal Reissner-Nordstrom black hole [13,14], (for the electromagnetic-gravitational/scalar perturbations). We focus on the question of whether the gap in the spacing in the imaginary part of the QNM frequencies has a well defined limit as n goes to infinity and if so, what is the value of the limit. The existence and the value of this limit has a crucial importance from the point of view of the currently popular Maggiore's conjecture, which represents a way of connecting the asymptotic behavior of the quasi-normal frequencies to the black hole thermodynamics. With the help of previous results and insights from the paper [16] we will prove that the gap between the imaginary parts of the frequencies does not converge to any limit, unless one puts specific constraints on the ratio of the two surface gravities related to the two spacetime horizons. Specifically the constraints are that the ratio of the surface gravi...
Institute of Scientific and Technical Information of China (English)
Li Xiao-Jing
2008-01-01
This paper studies a time delay equation for sea-air oscillator model. The existence and asymptotic estimates of periodic solutions of corresponding problem are obtained by employing the technique of upper and lower solution, and by using the continuation theorem of coincidence degree theory.
Parameter estimation and forecasting for multiplicative log-normal cascades.
Leövey, Andrés E; Lux, Thomas
2012-04-01
We study the well-known multiplicative log-normal cascade process in which the multiplication of Gaussian and log normally distributed random variables yields time series with intermittent bursts of activity. Due to the nonstationarity of this process and the combinatorial nature of such a formalism, its parameters have been estimated mostly by fitting the numerical approximation of the associated non-Gaussian probability density function to empirical data, cf. Castaing et al. [Physica D 46, 177 (1990)]. More recently, alternative estimators based upon various moments have been proposed by Beck [Physica D 193, 195 (2004)] and Kiyono et al. [Phys. Rev. E 76, 041113 (2007)]. In this paper, we pursue this moment-based approach further and develop a more rigorous generalized method of moments (GMM) estimation procedure to cope with the documented difficulties of previous methodologies. We show that even under uncertainty about the actual number of cascade steps, our methodology yields very reliable results for the estimated intermittency parameter. Employing the Levinson-Durbin algorithm for best linear forecasts, we also show that estimated parameters can be used for forecasting the evolution of the turbulent flow. We compare forecasting results from the GMM and Kiyono et al.'s procedure via Monte Carlo simulations. We finally test the applicability of our approach by estimating the intermittency parameter and forecasting of volatility for a sample of financial data from stock and foreign exchange markets.
Directory of Open Access Journals (Sweden)
Archana V
2014-05-01
Full Text Available Co-efficient of variation is a unitless measure of dispersion and is very frequently used in scientific investigations. This has motivated several researchers to propose estimators and tests concerning the co-efficient of variation of normal distribution(s. While proposing a class of estimators for the co-efficient of variation of a finite population, Tripathi et al., (2002 suggested that the estimator of co-efficient of variation of a finite population can also be used as an estimator of C.V for any distribution when the sampling design is SRSWR. This has motivated us to propose 28 estimators of finite population co-efficient of variation as estimators of co-efficient of variation of one component of a bivariate normal distribution when prior information is available regarding the second component. Cramer Rao type lower bound is derived to the mean square error of these estimators. Extensive simulation is carried out to compare these estimators. The results indicate that out of these 28 estimators, eight estimators have larger relative efficiency compared to the sample co-efficient of variation. The asymptotic mean square errors of the best estimators are derived to the order of for the benefit of users of co-efficient of variation.
Masmoudi, Nabil
2014-05-01
Traveltimes are conventionally evaluated by solving the zero-order approximation of the Wentzel, Kramers and Brillouin (WKB) expansion of the wave equation. This high frequency approximation is good enough for most imaging applications and provides us with a traveltime equation called the eikonal equation. The eikonal equation is a non-linear partial differential equation which can be solved by any of the familiar numerical methods. Among the most popular of these methods is the method of characteristics which yields the ray tracing equations and the finite difference approaches. In the first part of the Master Thesis, we use the ray tracing method to solve the eikonal equation to get P-waves traveltimes for orthorhombic models with arbitrary orientation of symmetry planes. We start with a ray tracing procedure specified in curvilinear coordinate system valid for anisotropy of arbitrary symmetry. The coordinate system is constructed so that the coordinate lines are perpendicular to the symmetry planes of an orthorohombic medium. Advantages of this approach are the conservation of orthorhombic symmetry throughout the model and reduction of the number of parameters specifying the model. We combine this procedure with first-order ray tracing and dynamic ray tracing equations for P waves propagating in smooth, inhomogeneous, weakly anisotropic media. The first-order ray tracing and dynamic ray tracing equations are derived from the exact ones by replacing the exact P-wave eigenvalue of the Christoffel matrix by its first-order approximation. In the second part of the Master Thesis, we compute traveltimes using the fast marching method and we develop an approach to estimate the anisotropy parameters. The idea is to relate them analytically to traveltimes which is challenging in inhomogeneous media. Using perturbation theory, we develop traveltime approximations for transversely isotropic media with horizontal symmetry axis (HTI) as explicit functions of the
DEFF Research Database (Denmark)
Vahdatirad, Mohammadjavad; Bayat, Mehdi; Andersen, Lars Vabbersgaard
2015-01-01
shear strength of clay. Normal and Sobol sampling are employed to provide the asymptotic sampling method to generate the probability distribution of the foundation stiffnesses. Monte Carlo simulation is used as a benchmark. Asymptotic sampling accompanied with Sobol quasi random sampling demonstrates...... an efficient method for estimating the probability distribution of stiffnesses for the offshore monopile foundation....
Measuring and Estimating Normalized Contrast in Infrared Flash Thermography
Koshti, Ajay M.
2013-01-01
Infrared flash thermography (IRFT) is used to detect void-like flaws in a test object. The IRFT technique involves heating up the part surface using a flash of flash lamps. The post-flash evolution of the part surface temperature is sensed by an IR camera in terms of pixel intensity of image pixels. The IR technique involves recording of the IR video image data and analysis of the data using the normalized pixel intensity and temperature contrast analysis method for characterization of void-like flaws for depth and width. This work introduces a new definition of the normalized IR pixel intensity contrast and normalized surface temperature contrast. A procedure is provided to compute the pixel intensity contrast from the camera pixel intensity evolution data. The pixel intensity contrast and the corresponding surface temperature contrast differ but are related. This work provides a method to estimate the temperature evolution and the normalized temperature contrast from the measured pixel intensity evolution data and some additional measurements during data acquisition.
The normal renal size of Korean children. Radiologic estimation
Energy Technology Data Exchange (ETDEWEB)
Ko, Young Tae; Hyun, Jae Suk; Kim, Young Sun; Kim, Kyung Do [Chungang University College of Medicine, Chinju (Korea, Republic of)
1995-05-01
A nephropathy following urinary tract infection is usually referred to as renal scarring. The main radiologic features are an overall reduction in the size of the kidney, with coarse scar, deformity of calyxes and indentation of the surface. If adequately treated, the progressive renal scarring by urinary tract infection could be prevented. Therefore, the early radiologic detection of renal damage following urinary tract infection or vesicoureteral reflux is great importance for the evaluation of the pathogenesis of renal scarring and for the planning of the therapy. To evaluate the renal damage, we must have the normal data of the kidneys. Many reports discussed the renal size in normal children, but there are no reports in the Korean children. We estimate the renal length, width, several focal parenchymal thicknesses for renal size evaluation and segmental lumbar vertebral length at the intravenous paleography in the normal Korean children. And the linear equations are obtained by the regression analysis between the various renal parameters and segmental vertebral length. Thereafter we make out the nomogram by the obtained equations. The renal length and width are highly correlated to the segmental lumbar vertebral length than various renal parenchymal thicknesses. These results suggest that the renal length and width are reliable parameters for normal renal size evaluation in growing kidney. And then the obtained equations and nomograms might be useful in the diagnosis of parenchymal loss in early scarring and follow-up. (author)
Normalized Minimum Error Entropy Algorithm with Recursive Power Estimation
Directory of Open Access Journals (Sweden)
Namyong Kim
2016-06-01
Full Text Available The minimum error entropy (MEE algorithm is known to be superior in signal processing applications under impulsive noise. In this paper, based on the analysis of behavior of the optimum weight and the properties of robustness against impulsive noise, a normalized version of the MEE algorithm is proposed. The step size of the MEE algorithm is normalized with the power of input entropy that is estimated recursively for reducing its computational complexity. The proposed algorithm yields lower minimum MSE (mean squared error and faster convergence speed simultaneously than the original MEE algorithm does in the equalization simulation. On the condition of the same convergence speed, its performance enhancement in steady state MSE is above 3 dB.
An algorithm for estimating surface normal from its boundary curves
Directory of Open Access Journals (Sweden)
Jisoon Park
2015-01-01
Full Text Available Recently, along with the improvements of geometry modeling methods using sketch-based interface, there have been a lot of developments in research about generating surface model from 3D curves. However, surfacing a 3D curve network remains an ambiguous problem due to the lack of geometric information. In this paper, we propose a new algorithm for estimating the normal vectors of the 3D curves which accord closely with user intent. Bending energy is defined by utilizing RMF(Rotation-Minimizing Frame of 3D curve, and we estimated this minimal energy frame as the one that accords design intent. The proposed algorithm is demonstrated with surface model creation of various curve networks. The algorithm of estimating geometric information in 3D curves which is proposed in this paper can be utilized to extract new information in the sketch-based modeling process. Also, a new framework of 3D modeling can be expected through the fusion between curve network and surface creating algorithm.
ASYMPTOTIC PROPERTIES OF MLE FOR WEIBULL DISTRIBUTION WITH GROUPED DATA
Institute of Scientific and Technical Information of China (English)
XUE Hongqi; SONG Lixin
2002-01-01
A grouped data model for Weibull distribution is considered. Under mild con-ditions, the maximum likelihood estimators(MLE) are shown to be identifiable, strongly consistent, asymptotically normal, and satisfy the law of iterated logarithm. Newton iter- ation algorithm is also considered, which converges to the unique solution of the likelihood equation. Moreover, we extend these results to a random case.
Asymptotics of the QMLE for General ARCH(q) Models
DEFF Research Database (Denmark)
Kristensen, Dennis; Rahbek, Anders Christian
2009-01-01
Asymptotics of the QMLE for Non-Linear ARCH Models Dennis Kristensen, Columbia University Anders Rahbek, University of Copenhagen Abstract Asymptotic properties of the quasi-maximum likelihood estimator (QMLE) for non-linear ARCH(q) models -- including for example Asymmetric Power ARCH and log......-ARCH -- are derived. Strong consistency is established under the assumptions that the ARCH process is geometrically ergodic, the conditional variance function has a finite log-moment, and finite second moment of the rescaled error. Asymptotic normality of the estimator is established under the additional assumption...... that certain ratios involving the conditional variance function are suitably bounded, and that the rescaled errors have little more than fourth moment. We verify our general conditions, including identification, for a wide range of leading specific ARCH models....
Asymptotic Markov inequality on Jordan arcs
Totik, V.
2017-03-01
Markov's inequality for the derivative of algebraic polynomials is considered on C^2-smooth Jordan arcs. The asymptotically best estimate is given for the kth derivative for all k=1,2,\\dots . The best constant is related to the behaviour around the endpoints of the arc of the normal derivative of the Green's function of the complementary domain. The result is deduced from the asymptotically sharp Bernstein inequality for the kth derivative at inner points of a Jordan arc, which is derived from a recent result of Kalmykov and Nagy on the Bernstein inequality on analytic arcs. In the course of the proof we shall also need to reduce the analyticity condition in this last result to C^2-smoothness. Bibliography: 21 titles.
Sass, D. A.; Schmitt, T. A.; Walker, C. M.
2008-01-01
Item response theory (IRT) procedures have been used extensively to study normal latent trait distributions and have been shown to perform well; however, less is known concerning the performance of IRT with non-normal latent trait distributions. This study investigated the degree of latent trait estimation error under normal and non-normal…
Sass, D. A.; Schmitt, T. A.; Walker, C. M.
2008-01-01
Item response theory (IRT) procedures have been used extensively to study normal latent trait distributions and have been shown to perform well; however, less is known concerning the performance of IRT with non-normal latent trait distributions. This study investigated the degree of latent trait estimation error under normal and non-normal…
Estimating the normal background rate of species extinction.
De Vos, Jurriaan M; Joppa, Lucas N; Gittleman, John L; Stephens, Patrick R; Pimm, Stuart L
2015-04-01
A key measure of humanity's global impact is by how much it has increased species extinction rates. Familiar statements are that these are 100-1000 times pre-human or background extinction levels. Estimating recent rates is straightforward, but establishing a background rate for comparison is not. Previous researchers chose an approximate benchmark of 1 extinction per million species per year (E/MSY). We explored disparate lines of evidence that suggest a substantially lower estimate. Fossil data yield direct estimates of extinction rates, but they are temporally coarse, mostly limited to marine hard-bodied taxa, and generally involve genera not species. Based on these data, typical background loss is 0.01 genera per million genera per year. Molecular phylogenies are available for more taxa and ecosystems, but it is debated whether they can be used to estimate separately speciation and extinction rates. We selected data to address known concerns and used them to determine median extinction estimates from statistical distributions of probable values for terrestrial plants and animals. We then created simulations to explore effects of violating model assumptions. Finally, we compiled estimates of diversification-the difference between speciation and extinction rates for different taxa. Median estimates of extinction rates ranged from 0.023 to 0.135 E/MSY. Simulation results suggested over- and under-estimation of extinction from individual phylogenies partially canceled each other out when large sets of phylogenies were analyzed. There was no evidence for recent and widespread pre-human overall declines in diversity. This implies that average extinction rates are less than average diversification rates. Median diversification rates were 0.05-0.2 new species per million species per year. On the basis of these results, we concluded that typical rates of background extinction may be closer to 0.1 E/MSY. Thus, current extinction rates are 1,000 times higher than natural
Estimating the Number of Clusters via Normalized Cluster Instability
Haslbeck, Jonas M. B.; Wulff, Dirk U.
2016-01-01
We improve existing instability-based methods for the selection of the number of clusters $k$ in cluster analysis by normalizing instability. In contrast to existing instability methods which only perform well for bounded sequences of small $k$, our method performs well across the whole sequence of possible $k$. In addition, we compare for the first time model-based and model-free variants of $k$ selection via cluster instability and find that their performance is similar. We make our method ...
Lenart, Łukasz
2011-01-01
The aim of this article is to establish asymptotic distributions and consistency of subsampling for spectral density and for magnitude of coherence for non-stationary, almost periodically correlated time series. We show the asymptotic normality of the spectral density estimator and the limiting distribution of a magnitude of coherence statistic for all points from the bifrequency square. The theoretical results hold under $\\alpha$-mixing and moment conditions.
DEFF Research Database (Denmark)
Vahdatirad, Mohammadjavad; Bayat, Mehdi; Andersen, Lars Vabbersgaard
2012-01-01
undrained shear strength. The random field is applied to represent the spatial variation of the soil properties. Monte Carlo simulation associate with an improved asymptotic sampling using normal and sobol sampling is utilized to generate the probability distribution of the foundation stiffness. It is shown...... that asymptotic sampling associated with sobol quasi random sampling is an efficient method to estimation of probability distribution in presented problems....
Energy Technology Data Exchange (ETDEWEB)
Shao, Kan, E-mail: Shao.Kan@epa.gov [ORISE Postdoctoral Fellow, National Center for Environmental Assessment, U.S. Environmental Protection Agency, Research Triangle Park, NC (United States); Gift, Jeffrey S. [National Center for Environmental Assessment, U.S. Environmental Protection Agency, Research Triangle Park, NC (United States); Setzer, R. Woodrow [National Center for Computational Toxicology, U.S. Environmental Protection Agency, Research Triangle Park, NC (United States)
2013-11-01
Continuous responses (e.g. body weight) are widely used in risk assessment for determining the benchmark dose (BMD) which is used to derive a U.S. EPA reference dose. One critical question that is not often addressed in dose–response assessments is whether to model the continuous data as normally or log-normally distributed. Additionally, if lognormality is assumed, and only summarized response data (i.e., mean ± standard deviation) are available as is usual in the peer-reviewed literature, the BMD can only be approximated. In this study, using the “hybrid” method and relative deviation approach, we first evaluate six representative continuous dose–response datasets reporting individual animal responses to investigate the impact on BMD/BMDL estimates of (1) the distribution assumption and (2) the use of summarized versus individual animal data when a log-normal distribution is assumed. We also conduct simulation studies evaluating model fits to various known distributions to investigate whether the distribution assumption has influence on BMD/BMDL estimates. Our results indicate that BMDs estimated using the hybrid method are more sensitive to the distribution assumption than counterpart BMDs estimated using the relative deviation approach. The choice of distribution assumption has limited impact on the BMD/BMDL estimates when the within dose-group variance is small, while the lognormality assumption is a better choice for relative deviation method when data are more skewed because of its appropriateness in describing the relationship between mean and standard deviation. Additionally, the results suggest that the use of summarized data versus individual response data to characterize log-normal distributions has minimal impact on BMD estimates. - Highlights: • We investigate to what extent the distribution assumption can affect BMD estimates. • Both real data analysis and simulation study are conducted. • BMDs estimated using hybrid method are more
THE SUPERIORITY OF EMPIRICAL BAYES ESTIMATION OF PARAMETERS IN PARTITIONED NORMAL LINEAR MODEL
Institute of Scientific and Technical Information of China (English)
Zhang Weiping; Wei Laisheng
2008-01-01
In this article, the empirical Bayes (EB) estimators are constructed for the estimable functions of the parameters in partitioned normal linear model. The superiorities of the EB estimators over ordinary least-squares (LS) estimator are investigated under mean square error matrix (MSEM) criterion.
Shao, Kan; Gift, Jeffrey S; Setzer, R Woodrow
2013-11-01
Continuous responses (e.g. body weight) are widely used in risk assessment for determining the benchmark dose (BMD) which is used to derive a U.S. EPA reference dose. One critical question that is not often addressed in dose-response assessments is whether to model the continuous data as normally or log-normally distributed. Additionally, if lognormality is assumed, and only summarized response data (i.e., mean±standard deviation) are available as is usual in the peer-reviewed literature, the BMD can only be approximated. In this study, using the "hybrid" method and relative deviation approach, we first evaluate six representative continuous dose-response datasets reporting individual animal responses to investigate the impact on BMD/BMDL estimates of (1) the distribution assumption and (2) the use of summarized versus individual animal data when a log-normal distribution is assumed. We also conduct simulation studies evaluating model fits to various known distributions to investigate whether the distribution assumption has influence on BMD/BMDL estimates. Our results indicate that BMDs estimated using the hybrid method are more sensitive to the distribution assumption than counterpart BMDs estimated using the relative deviation approach. The choice of distribution assumption has limited impact on the BMD/BMDL estimates when the within dose-group variance is small, while the lognormality assumption is a better choice for relative deviation method when data are more skewed because of its appropriateness in describing the relationship between mean and standard deviation. Additionally, the results suggest that the use of summarized data versus individual response data to characterize log-normal distributions has minimal impact on BMD estimates.
Seevers, P.M.; Ottmann, R. W.
1994-01-01
Evapotranspiration of irrigated crops on two irrigation service areas along the lower Colorado River was estimated using a normalized difference vegetation index of satellite data. A procedure was developed which equated the index to crop coefficients. Evapotranspiration estimates for fields for three dates of thematic mapper data were highly correlated with ground estimates. Service area estimates using thematic mapper and Advanced Very High Resolution Radiometer data agreed well with estimates based on US Geological Survey gauging station data.
Estimating differential quantities from point cloud based on a linear fitting of normal vectors
Institute of Scientific and Technical Information of China (English)
CHENG ZhangLin; ZHANG XiaoPeng
2009-01-01
Estimation of differential geometric properties on a discrete surface Is a fundamental work in computer graphics and computer vision.In this paper,we present an accurate and robust method for estimating differential quantities from unorganized point cloud.The principal curvatures and principal directions at each point are computed with the help of partial derivatives of the unit normal vector at that point,where the normal derivatives are estimated by fitting a linear function to each component of the normal vectors in a neighborhood.This method takes into account the normal information of all neighboring points and computes curvatures directly from the varlation of unit normal vectors,which improves the accuracy and robustness of curvature estimation on irregular sampled noisy data.The main advantage of our approach is that the estimation of curvatures at a point does not rely on the accuracy of the normal vector at that point,and the normal vectors can he refined In the process of curvature estimation.Compared with the state of the art methods for estimating curvatures and Darboux frames on both synthetic and real point clouds,the approach is shown to be more accurate and robust for noisy and unorganized point cloud data.
ASYMPTOTIC PROPERTIES OF MLE FOR WEIBULL DISTRIBUTION WITH GROUPED DATA
Institute of Scientific and Technical Information of China (English)
XUEHongqi; SONGLixin
2002-01-01
A grouped data model for weibull distribution is considered.Under mild conditions .the maximum likelihood estimators(MLE)are shown to be identifiable,strongly consistent,asymptotically normal,and satisfy the law of iterated logarithm .Newton iteration algorthm is also condsidered,which converges to the unique solution of the likelihood equation.Moreover,we extend these results to a random case.
Object Detection and Tracking-Based Camera Calibration for Normalized Human Height Estimation
Directory of Open Access Journals (Sweden)
Jaehoon Jung
2016-01-01
Full Text Available This paper presents a normalized human height estimation algorithm using an uncalibrated camera. To estimate the normalized human height, the proposed algorithm detects a moving object and performs tracking-based automatic camera calibration. The proposed method consists of three steps: (i moving human detection and tracking, (ii automatic camera calibration, and (iii human height estimation and error correction. The proposed method automatically calibrates camera by detecting moving humans and estimates the human height using error correction. The proposed method can be applied to object-based video surveillance systems and digital forensic.
Asymptotic inference in system identification for the atom maser.
Catana, Catalin; van Horssen, Merlijn; Guta, Madalin
2012-11-28
System identification is closely related to control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e. estimating a channel by probing it repeatedly with different input states. However, for quantum dynamical systems such as quantum Markov processes, it is more natural to consider the estimation based on continuous measurements of the output, with a given input that may be stationary. We address this problem using asymptotic statistics tools, for the specific example of estimating the Rabi frequency of an atom maser. We compute the Fisher information of different measurement processes as well as the quantum Fisher information of the atom maser, and establish the local asymptotic normality of these statistical models. The statistical notions can be expressed in terms of spectral properties of certain deformed Markov generators, and the connection to large deviations is briefly discussed.
Asymptotic inference in system identification for the atom maser
Catana, Catalin; Guta, Madalin
2011-01-01
System identification is an integrant part of control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e. estimating a channel by probing it repeatedly with different input states. However for quantum dynamical systems like quantum Markov processes, it is more natural to consider the estimation based on continuous measurements of the output, with a given input which may be stationary. We address this problem using asymptotic statistics tools, for the specific example of estimating the Rabi frequency of an atom maser. We compute the Fisher information of different measurement processes as well as the quantum Fisher information of the atom maser, and establish the local asymptotic normality of these statistical models. The statistical notions can be expressed in terms of spectral properties of certain deformed Markov generators and the connection to large deviations is briefly discussed.
Penrose type inequalities for asymptotically hyperbolic graphs
Dahl, Mattias; Sakovich, Anna
2013-01-01
In this paper we study asymptotically hyperbolic manifolds given as graphs of asymptotically constant functions over hyperbolic space $\\bH^n$. The graphs are considered as subsets of $\\bH^{n+1}$ and carry the induced metric. For such manifolds the scalar curvature appears in the divergence of a 1-form involving the integrand for the asymptotically hyperbolic mass. Integrating this divergence we estimate the mass by an integral over an inner boundary. In case the inner boundary satisfies a convexity condition this can in turn be estimated in terms of the area of the inner boundary. The resulting estimates are similar to the conjectured Penrose inequality for asymptotically hyperbolic manifolds. The work presented here is inspired by Lam's article concerning the asymptotically Euclidean case.
Asymptotics of trimmed CUSUM statistics
Berkes, István; Schauer, Johannes; 10.3150/10-BEJ318
2012-01-01
There is a wide literature on change point tests, but the case of variables with infinite variances is essentially unexplored. In this paper we address this problem by studying the asymptotic behavior of trimmed CUSUM statistics. We show that in a location model with i.i.d. errors in the domain of attraction of a stable law of parameter $0<\\alpha <2$, the appropriately trimmed CUSUM process converges weakly to a Brownian bridge. Thus, after moderate trimming, the classical method for detecting change points remains valid also for populations with infinite variance. We note that according to the classical theory, the partial sums of trimmed variables are generally not asymptotically normal and using random centering in the test statistics is crucial in the infinite variance case. We also show that the partial sums of truncated and trimmed random variables have different asymptotic behavior. Finally, we discuss resampling procedures which enable one to determine critical values in the case of small and mo...
Tail Probabilities for Registration Estimators
T. Mikosch; C.G. de Vries (Casper)
2006-01-01
textabstractEstimators of regression coefficients are known to be asymptotically normally distributed, provided certain regularity conditions are satisfied. In small samples and if the noise is not normally distributed, this can be a poor guide to the quality of the estimators. The paper addresses
Least squares with non-normal data: estimating experimental variance functions.
Tellinghuisen, Joel
2008-02-01
Contrary to popular belief, the method of least squares (LS) does not require that the data have normally distributed (Gaussian) error for its validity. One practically important application of LS fitting that does not involve normal data is the estimation of data variance functions (VFE) from replicate statistics. If the raw data are normal, sampling estimates s(2) of the variance sigma(2) are chi(2) distributed. For small degrees of freedom, the chi(2) distribution is strongly asymmetrical -- exponential in the case of three replicates, for example. Monte Carlo computations for linear variance functions demonstrate that with proper weighting, the LS variance-function parameters remain unbiased, minimum-variance estimates of the true quantities. However, the parameters are strongly non-normal -- almost exponential for some parameters estimated from s(2) values derived from three replicates, for example. Similar LS estimates of standard deviation functions from estimated s values have a predictable and correctable bias stemming from the bias inherent in s as an estimator of sigma. Because s(2) and s have uncertainties proportional to their magnitudes, the VFE and SDFE fits require weighting as s(-4) and s(-2), respectively. However, these weights must be evaluated on the calculated functions rather than directly from the sampling estimates. The computation is thus iterative but usually converges in a few cycles, with remaining 'weighting' bias sufficiently small as to be of no practical consequence.
Asymptotically Safe Dark Matter
DEFF Research Database (Denmark)
Sannino, Francesco; Shoemaker, Ian M.
2015-01-01
We introduce a new paradigm for dark matter (DM) interactions in which the interaction strength is asymptotically safe. In models of this type, the coupling strength is small at low energies but increases at higher energies, and asymptotically approaches a finite constant value. The resulting...... searches are the primary ways to constrain or discover asymptotically safe dark matter....
Asymptotically Safe Dark Matter
DEFF Research Database (Denmark)
Sannino, Francesco; Shoemaker, Ian M.
2015-01-01
We introduce a new paradigm for dark matter (DM) interactions in which the interaction strength is asymptotically safe. In models of this type, the coupling strength is small at low energies but increases at higher energies, and asymptotically approaches a finite constant value. The resulting...... searches are the primary ways to constrain or discover asymptotically safe dark matter....
The asymptotic distributions of the statistics of the skew elliptical variables
Institute of Scientific and Technical Information of China (English)
FANG Biqi
2005-01-01
In this paper, the asymptotic properties of the quadratic forms and the T statistic of the skew elliptical variables are studied. Consistent estimators of some parameters are obtained. The robustness of the significance level of the one-sided t test within the family of the skew normal family is investigated.
Directory of Open Access Journals (Sweden)
Sidi Ali Ould Abdi
2011-01-01
Full Text Available Given a stationary multidimensional spatial process (i=(i,i∈ℝ×ℝ,i∈ℤ, we investigate a kernel estimate of the spatial conditional quantile function of the response variable i given the explicative variable i. Asymptotic normality of the kernel estimate is obtained when the sample considered is an -mixing sequence.
Parallelism, Uniqueness, and Large-Sample Asymptotics for the Dantzig Selector
Dicker, Lee
2012-01-01
The Dantzig selector (Candes and Tao, 2007) is a popular l1-regularization method for variable selection and estimation in linear regression. We present a very weak geometric condition on the observed predictors which is related to parallelism and, when satisfied, ensures the uniqueness of Dantzig selector estimators. The condition holds with probability 1, if the predictors are drawn from a continuous distribution. We discuss the necessity of this condition for uniqueness and also provide a closely related condition which ensures uniqueness of lasso estimators (Tibshirani, 1996). Large sample asymptotics for the Dantzig selector, i.e. almost sure convergence and the asymptotic distribution, follow directly from our uniqueness results and a continuity argument. The limiting distribution of the Dantzig selector is generally non-normal. Though our asymptotic results require that the number of predictors is fixed (similar to (Knight and Fu, 2000)), our uniqueness results are valid for an arbitrary number of pred...
Estimator and tests for common coefficients of variation in normal distributions
Forkman, Johannes
2009-01-01
Inference for the coefficient of variation in normal distributions is considered. An explicit estimator of a coefficient of variation that is shared by several populations with normal distributions is proposed. Methods for making confidence intervals and statistical tests, based on McKay's approximation for the coefficient of variation, are provided. Exact expressions for the first two moments of McKay's approximation are given. An approximate F-test for equality of a coefficient of variation...
A Note on Parameter Estimations of Panel Vector Autoregressive Models with Intercorrelation
Institute of Scientific and Technical Information of China (English)
Jian-hong Wu; Li-xing Zhu; Zai-xing Li
2009-01-01
This note considers parameter estimation for panel vector autoregressive models with intercorrela-tion. Conditional least squares estimators are derived and the asymptotic normality is established. A simulation is carried out for illustration.
Normalized least-squares estimation in time-varying ARCH models
Fryzlewicz, Piotr; Sapatinas, Theofanis; Subba Rao, Suhasini
2008-01-01
We investigate the time-varying ARCH (tvARCH) process. It is shown that it can be used to describe the slow decay of the sample autocorrelations of the squared returns often observed in financial time series, which warrants the further study of parameter estimation methods for the model. ¶ Since the parameters are changing over time, a successful estimator needs to perform well for small samples. We propose a kernel normalized-least-squares (kernel-NLS) estimator which has a closed form...
An asymptotic model of the F layer
Oliver, W. L.
2012-01-01
A model of the F layer of the ionosphere is presented that consists of a bottomside asymptote that ignores transport and a topside asymptote that ignores chemistry. The asymptotes connect at the balance height dividing the chemistry and transport regimes. A combination of these two asymptotes produces a good approximation to the true F layer. Analogously, a model of F layer response to an applied vertical drift is presented that consists of two asymptotic responses, one that ignores transport and one that ignores chemistry. The combination of these asymptotic responses produces a good approximation to the response of the true F layer. This latter response is identical to the “servo” response of Rishbeth et al. (1978), derived from the continuity equation. The asymptotic approach bypasses the continuity equation in favor of “force balance” arguments and so replaces a differential equation with simpler algebraic equations. This new approach provides a convenient and intuitive mean for first-order estimates of the change in F layer peak height and density in terms of changes in neutral density, composition, temperature, winds, and electric fields. It is applicable at midlatitudes and at magnetically quiet times at high latitudes. Forensic inverse relations are possible but are not unique. The validity of the asymptotic relations is shown through numerical simulation.
Behavioral estimates of basilar-membrane input-output in normal-hearing listeners
DEFF Research Database (Denmark)
Jepsen, Morten Løve; Dau, Torsten
2011-01-01
To characterize human cochlear processing it would be beneficial to behaviorally estimate the basilar membrane (BM) input-output (I/O) function. In recent studies, forward masking has been used to estimate BM compression. In this study, a growth-of-forward-masking (GOM) paradigm (e.g., Oxenham...... function is expected than that obtained for a high-level signal where both masker and signal are processed compressively. The knee point can be estimated at the input level where the GOM slope changes significantly. Data were collected from seven normal - hearing listeners. The method was found to provide...... estimates of the BM I/O function for a wider range of input levels than in previously suggested methods, due to the additional estimates of the knee points....
Structure and asymptotic theory for nonlinear models with GARCH errors
Directory of Open Access Journals (Sweden)
Felix Chan
2015-01-01
Full Text Available Nonlinear time series models, especially those with regime-switching and/or conditionally heteroskedastic errors, have become increasingly popular in the economics and finance literature. However, much of the research has concentrated on the empirical applications of various models, with little theoretical or statistical analysis associated with the structure of the processes or the associated asymptotic theory. In this paper, we derive sufficient conditions for strict stationarity and ergodicity of three different specifications of the first-order smooth transition autoregressions with heteroskedastic errors. This is essential, among other reasons, to establish the conditions under which the traditional LM linearity tests based on Taylor expansions are valid. We also provide sufficient conditions for consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator for a general nonlinear conditional mean model with first-order GARCH errors.
Asymptotics of Random Contractions
Hashorva, Enkelejd; Tang, Qihe
2010-01-01
In this paper we discuss the asymptotic behaviour of random contractions $X=RS$, where $R$, with distribution function $F$, is a positive random variable independent of $S\\in (0,1)$. Random contractions appear naturally in insurance and finance. Our principal contribution is the derivation of the tail asymptotics of $X$ assuming that $F$ is in the max-domain of attraction of an extreme value distribution and the distribution function of $S$ satisfies a regular variation property. We apply our result to derive the asymptotics of the probability of ruin for a particular discrete-time risk model. Further we quantify in our asymptotic setting the effect of the random scaling on the Conditional Tail Expectations, risk aggregation, and derive the joint asymptotic distribution of linear combinations of random contractions.
Composite Operators in Asymptotic Safety
Pagani, Carlo
2016-01-01
We study the role of composite operators in the Asymptotic Safety program for quantum gravity. By including in the effective average action an explicit dependence on new sources we are able to keep track of operators which do not belong to the exact theory space and/or are normally discarded in a truncation. Typical examples are geometric operators such as volumes, lengths, or geodesic distances. We show that this set-up allows to investigate the scaling properties of various interesting operators via a suitable exact renormalization group equation. We test our framework in several settings, including Quantum Einstein Gravity, the conformally reduced Einstein-Hilbert truncation, and two dimensional quantum gravity. Finally, we briefly argue that our construction paves the way to approach observables in the Asymptotic Safety program.
Sandberg, Mattias
2015-01-07
The Monte Carlo (and Multi-level Monte Carlo) finite element method can be used to approximate observables of solutions to diffusion equations with log normal distributed diffusion coefficients, e.g. modelling ground water flow. Typical models use log normal diffusion coefficients with H¨older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible and can be larger than the computable low frequency error. This talk will address how the total error can be estimated by the computable error.
Comparison of methods of estimating body fat in normal subjects and cancer patients
Energy Technology Data Exchange (ETDEWEB)
Cohn, S.H. (Brookhaven National Lab., Upton, NY); Ellis, K.J.; Vartsky, D.; Sawitsky, A.; Gartenhaus, W.; Yasumura, S.; Vaswani, A.N.
1981-12-01
Total body fat can be indirectly estimated by the following noninvasive techniques: determination of lean body mass by measurement of body potassium or body water, and determination of density by underwater weighing or by skinfold measurements. The measurement of total body nitrogen by neutron activation provides another technique for estimating lean body mass and hence body fat. The nitrogen measurement can also be combined with the measurement of total body potassium in a two compartment model of the lean body mass from which another estimate of body fat can be derived. All of the above techniques are subject to various errors and are based on a number of assumptions, some of which are incompletely validated. These techniques were applied to a population of normal subjects and to a group of cancer patients. The advantages and disadvantages of each method are discussed in terms of their ability to estimate total body fat.
Comparison of methods of estimating body fat in normal subjects and cancer patients.
Cohn, S H; Ellis, K J; Vartsky, D; Sawitsky, A; Gartenhaus, W; Yasumura, S; Vaswani, A N
1981-12-01
Total body fat can be indirectly estimated by the following noninvasive techniques: determination of lean body mass by measurement of body potassium or body water, and determination of density by underwater weighing or by skinfold measurements. The measurement of total body nitrogen by neutron activation provides another technique for estimating lean body mass and hence body fat. The nitrogen measurement can also be combined with the measurement of total body potassium in a two compartment model of the lean body mass from which another estimate of body fat can be derived. All of the above techniques are subject to various errors and are based on a number of assumptions, some of which are incompletely validated. These techniques were applied to a population of normal subjects and to a group of cancer patients. The advantages and disadvantages of each method are discussed in terms of their ability to estimate total body fat.
ASYMPTOTIC QUANTIZATION OF PROBABILITY DISTRIBUTIONS
Institute of Scientific and Technical Information of China (English)
Klaus P(o)tzelberger
2003-01-01
We give a brief introduction to results on the asymptotics of quantization errors.The topics discussed include the quantization dimension,asymptotic distributions of sets of prototypes,asymptotically optimal quantizations,approximations and random quantizations.
Estimation Normal Vector of Triangular Mesh Vertex by Angle and Centroid Weights and its Application
Directory of Open Access Journals (Sweden)
Yueping Chen
2013-04-01
Full Text Available To compute vertex normal of triangular meshes more accurately, this paper presents an improved algorithm based on angle and centroid weights. Firstly, four representational algorithms are analyzed by comparing their weighting characteristics such as angles, areas and centroids. The drawbacks of each algorithm are discussed. Following that, an improved algorithm is put forward based on angle and centroid weights. Finally, by taking the deviation angle between the nominal normal vector and the estimated one as the error evaluation standard factor, the triangular mesh models of spheres, ellipsoids, paraboloids and cylinders are used to analyze the performance of all these estimation algorithms. The machining and inspection operations of one mould part are conducted to verify the improved algorithm. Experimental results demonstrate that the algorithm is effective.
Statistical Tests for the Reciprocal of a Normal Mean with a Known Coefficient of Variation
Directory of Open Access Journals (Sweden)
Wararit Panichkitkosolkul
2015-01-01
Full Text Available An asymptotic test and an approximate test for the reciprocal of a normal mean with a known coefficient of variation were proposed in this paper. The asymptotic test was based on the expectation and variance of the estimator of the reciprocal of a normal mean. The approximate test used the approximate expectation and variance of the estimator by Taylor series expansion. A Monte Carlo simulation study was conducted to compare the performance of the two statistical tests. Simulation results showed that the two proposed tests performed well in terms of empirical type I errors and power. Nevertheless, the approximate test was easier to compute than the asymptotic test.
On the estimation of the structure parameter of a normal distribution of order p
Directory of Open Access Journals (Sweden)
Angelo M. Mineo
2007-10-01
Full Text Available In this paper we compare four different approaches to estimate the structure parameter of a normal distribution of order p (often called exponential power distribution. In particular, we have considered the maximization of the log-likelihood, of the profile log-likelihood, of the conditional profile log-likelihood and a method based on an index of kurtosis. The results of a simulation study seem to indicate the latter approach as the best.
Structural Vector Description and Estimation of Normal Boiling Points for 66 Aromatic Hydrocarbons
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A molecular vector-type descriptor containing 6 variables is used to describe the structure of aromatic hydrocarbons (AHs) and relate to normal boiling points (bp) of AHs. The correlation coefficient (R) between the estimated bp and experimental bp is 0.9988 and the root mean square error (RMS) is 7.907° C for 66 AHs. The RMS obtained by cross-validation is 9.131° C, which implies the relationship model having good prediction ability.
Li, Teng; Hong, Daxiang
2016-04-01
From three interferograms, a novel algorithm for extracting phase shifts based on the vector projection of normalized difference maps is presented. In it, subtraction and vector normalization are operated successively to obtain two normalized interferogram differences without the effect of background component. Then, the phase shift can be estimated based on the analysis and calculation of the vector projection. Without any iteration and complex calculation, this algorithm can be implemented for phase-shift range approximately being well distributed from 0 to 2π, when fringe number of interferograms is more than one. It offers a powerful tool for rapid calibration of phase shifts because of its high efficiency and easy implementation. Numerical simulations and experiments are performed to prove its validity.
Institute of Scientific and Technical Information of China (English)
许璐; 赵闻达
2012-01-01
运用古典概率的有关知识，通过建立合适的数学模型导出了复合二项分布的破产概率的显式解，进而得到了它的渐近估计表达式。所得结论包含了有关文献的结果。%The classical probability theory is used to derive solution of the ultimate ruin prob- ability in a compound binomial distribution model, and its asymptotic estimation is obtained. The conclusion has improved the result in related literature.
Estimation in partial linear EV models with replicated observations
Institute of Scientific and Technical Information of China (English)
CUI; Hengjian
2004-01-01
The aim of this work is to construct the parameter estimators in the partial linear errors-in-variables (EV) models and explore their asymptotic properties. Unlike other related References, the assumption of known error covariance matrix is removed when the sample can be repeatedly drawn at each designed point from the model. The estimators of interested regression parameters, and the model error variance, as well as the nonparametric function, are constructed. Under some regular conditions, all of the estimators prove strongly consistent. Meanwhile, the asymptotic normality for the estimator of regression parameter is also presented. A simulation study is reported to illustrate our asymptotic results.
Weakly asymptotically hyperbolic manifolds
Allen, Paul T; Lee, John M; Allen, Iva Stavrov
2015-01-01
We introduce a class of "weakly asymptotically hyperbolic" geometries whose sectional curvatures tend to $-1$ and are $C^0$, but are not necessarily $C^1$, conformally compact. We subsequently investigate the rate at which curvature invariants decay at infinity, identifying a conformally invariant tensor which serves as an obstruction to "higher order decay" of the Riemann curvature operator. Finally, we establish Fredholm results for geometric elliptic operators, extending the work of Rafe Mazzeo and John M. Lee to this setting. As an application, we show that any weakly asymptotically hyperbolic metric is conformally related to a weakly asymptotically hyperbolic metric of constant negative curvature.
Avila, M L; Koshchiy, E; Baby, L T; Belarge, J; Kemper, K W; Kuchera, A N; Mukhamedzhanov, A M; Santiago-Gonzalez, D; Uberseder, E
2014-01-01
Background. The $^{12}$C($\\alpha,\\gamma$)$^{16}$O reaction plays a fundamental role in astrophysics because its cross section near 300 keV in c.m. determines the $^{12}$C/$^{16}$O ratio at the end of the helium burning stage of stellar evolution. The astrophysically desired accuracy of better than 10\\% has not been achieved. Cascade $\\gamma$ transitions through the excited states of $^{16}$O are contributing to the uncertainty. Purpose. To measure the Asymptotic Normalization Coefficients (ANCs) for the 0$^+$ (6.05 MeV) and 3$^-$ (6.13 MeV) excited states in $^{16}$O and provide constraints on the cross section for the corresponding cascade transitions. Method. The ANCs were measured using the $\\alpha$-transfer reaction $^{12}$C($^6$Li,$d$)$^{16}$O performed at sub-Coulomb energies for both the entrance and exit channels. Results. The ANCs for the 0$^+$(6.05 MeV), 3$^-$(6.13 MeV), 2$^+$(6.92 MeV) and 1$^-$(7.12 MeV) states in $^{16}$O have been measured. The contribution of the 0$^+$ and 3$^-$ cascade transit...
Adamyan, Vadim M; Iserte, Jose L.; Tkachenko, Igor M.
2005-01-01
Asymptotic forms of the Hilbert-Scmidt and Hilbert norms of positive definite Toeplitz matrices $Q_{N}=(b(j-k))_{j,k=0}^{N-1}$ as $N\\to \\infty $ are determined. Here $b(j)$ are consequent trigonometric moments of a generating non-negative mesure $d\\sigma (\\theta)$ on $[ -\\pi ,\\pi ] $. It is proven that $\\sigma (\\theta)$ is continuous if and only if any of those contributions is $o(N)$. Analogous criteria are given for positive integral operators with difference kernels. Obtained results are a...
Directory of Open Access Journals (Sweden)
Howard Viator
2012-06-01
Full Text Available Estimating crop yield using remote sensing techniques has proven to be successful. However, sugarcane possesses unique characteristics; such as, a multi-year cropping cycle and plant height-limiting for midseason fertilizer application timing. Our study objective was to determine if sugarcane yield potential could be estimated using an in-season estimation of normalized difference vegetative index (NDVI. Sensor readings were taken using the GreenSeeker® handheld sensor from 2008 to 2011 in St. Gabriel and Jeanerette, LA, USA. In-season estimates of yield (INSEY values were calculated by dividing NDVI by thermal variables. Optimum timing for estimating sugarcane yield was between 601–750 GDD. In-season estimated yield values improved the yield potential (YP model compared to using NDVI. Generally, INSEY value showed a positive exponential relationship with yield (r^{2} values 0.48 and 0.42 for cane tonnage and sugar yield, respectively. When models were separated based on canopy structure there was an increase the strength of the relationship for the erectophile varieties (r^{2} 0.53 and 0.47 for cane tonnage and sugar yield, respectively; however, the model for planophile varieties weakened slightly. Results of this study indicate using an INSEY value for predicting sugarcane yield shows potential of being a valuable management tool for sugarcane producers in Louisiana.
Lofton, Josh; Tubana, Brenda S; Kanke, Yumiko; Teboh, Jasper; Viator, Howard; Dalen, Marilyn
2012-01-01
Estimating crop yield using remote sensing techniques has proven to be successful. However, sugarcane possesses unique characteristics; such as, a multi-year cropping cycle and plant height-limiting for midseason fertilizer application timing. Our study objective was to determine if sugarcane yield potential could be estimated using an in-season estimation of normalized difference vegetative index (NDVI). Sensor readings were taken using the GreenSeeker® handheld sensor from 2008 to 2011 in St. Gabriel and Jeanerette, LA, USA. In-season estimates of yield (INSEY) values were calculated by dividing NDVI by thermal variables. Optimum timing for estimating sugarcane yield was between 601-750 GDD. In-season estimated yield values improved the yield potential (YP) model compared to using NDVI. Generally, INSEY value showed a positive exponential relationship with yield (r(2) values 0.48 and 0.42 for cane tonnage and sugar yield, respectively). When models were separated based on canopy structure there was an increase the strength of the relationship for the erectophile varieties (r(2) 0.53 and 0.47 for cane tonnage and sugar yield, respectively); however, the model for planophile varieties weakened slightly. Results of this study indicate using an INSEY value for predicting sugarcane yield shows potential of being a valuable management tool for sugarcane producers in Louisiana.
Nonstandard asymptotic analysis
Berg, Imme
1987-01-01
This research monograph considers the subject of asymptotics from a nonstandard view point. It is intended both for classical asymptoticists - they will discover a new approach to problems very familiar to them - and for nonstandard analysts but includes topics of general interest, like the remarkable behaviour of Taylor polynomials of elementary functions. Noting that within nonstandard analysis, "small", "large", and "domain of validity of asymptotic behaviour" have a precise meaning, a nonstandard alternative to classical asymptotics is developed. Special emphasis is given to applications in numerical approximation by convergent and divergent expansions: in the latter case a clear asymptotic answer is given to the problem of optimal approximation, which is valid for a large class of functions including many special functions. The author's approach is didactical. The book opens with a large introductory chapter which can be read without much knowledge of nonstandard analysis. Here the main features of the t...
Efficient Estimation in Heteroscedastic Varying Coefficient Models
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Chuanhua Wei
2015-07-01
Full Text Available This paper considers statistical inference for the heteroscedastic varying coefficient model. We propose an efficient estimator for coefficient functions that is more efficient than the conventional local-linear estimator. We establish asymptotic normality for the proposed estimator and conduct some simulation to illustrate the performance of the proposed method.
Asymptotic normality of randomly truncated stochastic algorithms
Lelong, Jérôme
2010-01-01
We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins-Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to ensure convergence when standard algorithms fail because the expected-value function grows too fast. In this work, we give a self contained proof of a central limit theorem for this algorithm under local assumptions on the expected-value function, which are fairly easy to check in practice.
Asymptotic normality of randomly truncated stochastic algorithms
Lelong, Jérôme
2010-01-01
We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins-Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to ensure convergence when standard algorithms fail because the expected-value function grows too fast. In this work, we give a self contained proof of a central limit theorem for this algorithm under local assumptions on the expected-value function, which are fairly easy to check in practice.
The Semiparametric Normal Variance-Mean Mixture Model
DEFF Research Database (Denmark)
Korsholm, Lars
1997-01-01
We discuss the normal vairance-mean mixture model from a semi-parametric point of view, i.e. we let the mixing distribution belong to a non parametric family. The main results are consistency of the non parametric maximum likelihood estimat or in this case, and construction of an asymptotically...... normal and efficient estimator....
Large Deviations and Asymptotic Methods in Finance
Gatheral, Jim; Gulisashvili, Archil; Jacquier, Antoine; Teichmann, Josef
2015-01-01
Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find th...
Estimation of a multivariate normal mean with a bounded signal to noise ratio
Kortbi, Othmane
2012-01-01
For normal canonical models with $X \\sim N_p(\\theta, \\sigma^{2} I_{p}), \\;\\; S^{2} \\sim \\sigma^{2}\\chi^{2}_{k}, \\;{independent}$, we consider the problem of estimating $\\theta$ under scale invariant squared error loss $\\frac{\\|d-\\theta \\|^{2}}{\\sigma^{2}}$, when it is known that the signal-to-noise ratio $\\frac{\\|\\theta\\|}{\\sigma}$ is bounded above by $m$. Risk analysis is achieved by making use of a conditional risk decomposition and we obtain in particular sufficient conditions for an estimator to dominate either the unbiased estimator $\\delta_{UB}(X)=X$, or the maximum likelihood estimator $\\delta_{\\hbox{mle}}(X,S^2)$, or both of these benchmark procedures. The given developments bring into play the pivotal role of the boundary Bayes estimator $\\delta_{BU}$ associated with a prior on $(\\theta,\\sigma)$ such that $\\theta|\\sigma$ is uniformly distributed on the (boundary) sphere of radius $m$ and a non-informative $\\frac{1}{\\sigma}$ prior measure is placed marginally on $\\sigma$. With a series of technical re...
Slope Estimation during Normal Walking Using a Shank-Mounted Inertial Sensor
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Juan C. Álvarez
2012-08-01
Full Text Available In this paper we propose an approach for the estimation of the slope of the walking surface during normal walking using a body-worn sensor composed of a biaxial accelerometer and a uniaxial gyroscope attached to the shank. It builds upon a state of the art technique that was successfully used to estimate the walking velocity from walking stride data, but did not work when used to estimate the slope of the walking surface. As claimed by the authors, the reason was that it did not take into account the actual inclination of the shank of the stance leg at the beginning of the stride (mid stance. In this paper, inspired by the biomechanical characteristics of human walking, we propose to solve this issue by using the accelerometer as a tilt sensor, assuming that at mid stance it is only measuring the gravity acceleration. Results from a set of experiments involving several users walking at different inclinations on a treadmill confirm the feasibility of our approach. A statistical analysis of slope estimations shows in first instance that the technique is capable of distinguishing the different slopes of the walking surface for every subject. It reports a global RMS error (per-unit difference between actual and estimated inclination of the walking surface for each stride identified in the experiments of 0.05 and this can be reduced to 0.03 with subject-specific calibration and post processing procedures by means of averaging techniques.
Liu, X.; Beroza, G. C.; Ben-Zion, Y.
2016-12-01
We estimate the frequency-dependent amplitude error of ambient noise cross-correlations based on the method of Liu et al. (2016) for different normalizations. We compute the stacked cross spectrum of noise recorded at station pairs in southern California by averaging the cross spectrum of evenly spaced windows of the same length, but offset in time. Windows with signals (e.g. earthquakes) contaminating the ambient seismic noise are removed as statistical outliers. Standard errors of the real and imaginary parts of the stacked cross-spectrum are estimated assuming each window is independent. The autocorrelation of the sequence of cross-spectrum values at a given frequency obtained from different windows are used to test the independence of cross-spectrum values in neighboring time windows. For frequencies below 0.2 Hz, we find temporal correlation in the noise data. We account for temporal correlation in computation of errors using a block bootstrap resampling method. The stacked cross-spectrum and associated amplitude are computed under different normalization methods including deconvolution and whitening applied before or after ensemble average of cross-spectrum values. We estimate the amplitude errors based on error propagation from errors of stacked cross-spectrum and verified by bootstrap method. We propose to use this characterization of amplitude uncertainty to constrain uncertainties in ground motion predictions based on ambient-field observations.
Asymptotic distribution of ∆AUC, NRIs, and IDI based on theory of U-statistics.
Demler, Olga V; Pencina, Michael J; Cook, Nancy R; D'Agostino, Ralph B
2017-09-20
The change in area under the curve (∆AUC), the integrated discrimination improvement (IDI), and net reclassification index (NRI) are commonly used measures of risk prediction model performance. Some authors have reported good validity of associated methods of estimating their standard errors (SE) and construction of confidence intervals, whereas others have questioned their performance. To address these issues, we unite the ∆AUC, IDI, and three versions of the NRI under the umbrella of the U-statistics family. We rigorously show that the asymptotic behavior of ∆AUC, NRIs, and IDI fits the asymptotic distribution theory developed for U-statistics. We prove that the ∆AUC, NRIs, and IDI are asymptotically normal, unless they compare nested models under the null hypothesis. In the latter case, asymptotic normality and existing SE estimates cannot be applied to ∆AUC, NRIs, or IDI. In the former case, SE formulas proposed in the literature are equivalent to SE formulas obtained from U-statistics theory if we ignore adjustment for estimated parameters. We use Sukhatme-Randles-deWet condition to determine when adjustment for estimated parameters is necessary. We show that adjustment is not necessary for SEs of the ∆AUC and two versions of the NRI when added predictor variables are significant and normally distributed. The SEs of the IDI and three-category NRI should always be adjusted for estimated parameters. These results allow us to define when existing formulas for SE estimates can be used and when resampling methods such as the bootstrap should be used instead when comparing nested models. We also use the U-statistic theory to develop a new SE estimate of ∆AUC. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.
Directory of Open Access Journals (Sweden)
Edmond Zahedi
2015-01-01
Full Text Available The feasibility of a novel system to reliably estimate the normalized central blood pressure (CBPN from the radial photoplethysmogram (PPG is investigated. Right-wrist radial blood pressure and left-wrist PPG were simultaneously recorded in five different days. An industry-standard applanation tonometer was employed for recording radial blood pressure. The CBP waveform was amplitude-normalized to determine CBPN. A total of fifteen second-order autoregressive models with exogenous input were investigated using system identification techniques. Among these 15 models, the model producing the lowest coefficient of variation (CV of the fitness during the five days was selected as the reference model. Results show that the proposed model is able to faithfully reproduce CBPN (mean fitness = 85.2% ± 2.5% from the radial PPG for all 15 segments during the five recording days. The low CV value of 3.35% suggests a stable model valid for different recording days.
Model-integrated estimation of normal tissue contamination for cancer SNP allelic copy number data.
Stjernqvist, Susann; Rydén, Tobias; Greenman, Chris D
2011-01-01
SNP allelic copy number data provides intensity measurements for the two different alleles separately. We present a method that estimates the number of copies of each allele at each SNP position, using a continuous-index hidden Markov model. The method is especially suited for cancer data, since it includes the fraction of normal tissue contamination, often present when studying data from cancer tumors, into the model. The continuous-index structure takes into account the distances between the SNPs, and is thereby appropriate also when SNPs are unequally spaced. In a simulation study we show that the method performs favorably compared to previous methods even with as much as 70% normal contamination. We also provide results from applications to clinical data produced using the Affymetrix genome-wide SNP 6.0 platform.
Influence of thermal anisotropy on best-fit estimates of shock normals.
Lepping, R. P.
1972-01-01
This paper deals with the influence of thermal anisotropy on least-squares estimates of interplanetary shock parameters and the associated normals by using the Rankine-Hugoniot equations. A practical theorem is given for quantitatively correcting for anisotropic effects by weighting the before and after magnetic fields by the same 'anisotropy parameter' h. The quantity h depends only on the thermal anisotropies before and after the shock and on the angles between the magnetic fields and the shock normal. It is shown that, for fast shocks and for a liberal range of realistic conditions, the quantity h lies in the range from 0.90 to 1.22. The theorem can also be applied to most slow shocks, but in those instances h usually should be lower and sometimes markedly lower than unity.
On estimation of survival function under random censoring model
Institute of Scientific and Technical Information of China (English)
JIANG; Jiancheng(蒋建成); CHENG; Bo(程博); WU; Xizhi(吴喜之)
2002-01-01
We study an estimator of the survival function under the random censoring model. Bahadur-type representation of the estimator is obtained and asymptotic expression for its mean squared errors is given, which leads to the consistency and asymptotic normality of the estimator. A data-driven local bandwidth selection rule for the estimator is proposed. It is worth noting that the estimator is consistent at left boundary points, which contrasts with the cases of density and hazard rate estimation. A Monte Carlo comparison of different estimators is made and it appears that the proposed data-driven estimators have certain advantages over the common Kaplan-Meier estmator.
Directory of Open Access Journals (Sweden)
Rodrigo Moura Pereira
2016-06-01
Full Text Available Large farmland areas and the knowledge on the interaction between solar radiation and vegetation canopies have increased the use of data from orbital remote sensors in sugarcane monitoring. However, the constituents of the atmosphere affect the reflectance values obtained by imaging sensors. This study aimed at improving a sugarcane Leaf Area Index (LAI estimation model, concerning the Normalized Difference Vegetation Index (NDVI subjected to atmospheric correction. The model generated by the NDVI with atmospheric correction showed the best results (R2 = 0.84; d = 0.95; MAE = 0.44; RMSE = 0.55, in relation to the other models compared. LAI estimation with this model, during the sugarcane plant cycle, reached a maximum of 4.8 at the vegetative growth phase and 2.3 at the end of the maturation phase. Thus, the use of atmospheric correction to estimate the sugarcane LAI is recommended, since this procedure increases the correlations between the LAI estimated by image and by plant parameters.
Binder, Hans; Brücker, Jan; Burden, Conrad J
2009-03-05
The problem of inferring accurate quantitative estimates of transcript abundances from gene expression microarray data is addressed. Particular attention is paid to correcting chip-to-chip variations arising mainly as a result of unwanted nonspecific background hybridization to give transcript abundances measured in a common scale. This study verifies and generalizes a model of the mutual dependence between nonspecific background hybridization and the sensitivity of the specific signal using an approach based on the physical chemistry of surface hybridization. We have analyzed GeneChip oligonucleotide microarray data taken from a set of five benchmark experiments including dilution, Latin Square, and "Golden spike" designs. Our analysis concentrates on the important effect of changes in the unwanted nonspecific background inherent in the technology due to changes in total RNA target concentration and/or composition. We find that incremental changes in nonspecific background entail opposite sign incremental changes in the effective specific binding constant. This effect, which we refer to as the "up-down" effect, results from the subtle interplay of competing interactions between the probes and specific and nonspecific targets at the chip surface and in bulk solution. We propose special rules for proper normalization of expression values considering the specifics of the up-down effect. Particularly for normalization one has to level the expression values of invariant expressed probes. Existing heuristic normalization techniques which do not exclude absent probes, level intensities instead of expression values, and/or use low variance criteria for identifying invariant sets of probes lead to biased results. Strengths and pitfalls of selected normalization methods are discussed. We also find that the extent of the up-down effect is modified if RNA targets are replaced by DNA targets, in that microarray sensitivity and specificity are improved via a decrease in
Edgeworth expansion for the survival function estimator in the Koziol-Green model
Institute of Scientific and Technical Information of China (English)
SUN; Liuquan(孙六全); WU; Guofu(吴国富)
2002-01-01
In the KozioI-Green or proportional hazards random censorship model, the asymptotic accuracy of the estimated one-term Edgeworth expansion and the smoothed bootstrap approximation for the Studen tized Abdushukurov-Cheng-Lin estimator is investigated. It is shown that both the Edgeworth expansion estimate and the bootstrap approximation are asymptotically closer to the exact distribution of the Studentized Abdushukurov-Cheng-Lin estimator than the normal approximation.
A non-parametric approach to estimate the total deviation index for non-normal data.
Perez-Jaume, Sara; Carrasco, Josep L
2015-11-10
Concordance indices are used to assess the degree of agreement between different methods that measure the same characteristic. In this context, the total deviation index (TDI) is an unscaled concordance measure that quantifies to which extent the readings from the same subject obtained by different methods may differ with a certain probability. Common approaches to estimate the TDI assume data are normally distributed and linearity between response and effects (subjects, methods and random error). Here, we introduce a new non-parametric methodology for estimation and inference of the TDI that can deal with any kind of quantitative data. The present study introduces this non-parametric approach and compares it with the already established methods in two real case examples that represent situations of non-normal data (more specifically, skewed data and count data). The performance of the already established methodologies and our approach in these contexts is assessed by means of a simulation study. Copyright © 2015 John Wiley & Sons, Ltd.
Skinner, R.H.; Wylie, B.K.; Gilmanov, T.G.
2011-01-01
Satellite-based normalized difference vegetation index (NDVI) data have been extensively used for estimating gross primary productivity (GPP) and yield of grazing lands throughout the world. However, the usefulness of satellite-based images for monitoring rotationally-grazed pastures in the northeastern United States might be limited because paddock size is often smaller than the resolution limits of the satellite image. This research compared NDVI data from satellites with data obtained using a ground-based system capable of fine-scale (submeter) NDVI measurements. Gross primary productivity was measured by eddy covariance on two pastures in central Pennsylvania from 2003 to 2008. Weekly 250-m resolution satellite NDVI estimates were also obtained for each pasture from the moderate resolution imaging spectroradiometer (MODIS) sensor. Ground-based NDVI data were periodically collected in 2006, 2007, and 2008 from one of the two pastures. Multiple-regression and regression-tree estimates of GPP, based primarily on MODIS 7-d NDVI and on-site measurements of photosynthetically active radiation (PAR), were generally able to predict growing-season GPP to within an average of 3% of measured values. The exception was drought years when estimated and measured GPP differed from each other by 11 to 13%. Ground-based measurements improved the ability of vegetation indices to capture short-term grazing management effects on GPP. However, the eMODIS product appeared to be adequate for regional GPP estimates where total growing-season GPP across a wide area would be of greater interest than short-term management-induced changes in GPP at individual sites.
Ramnath, Rudrapatna V
2012-01-01
This book addresses the task of computation from the standpoint of asymptotic analysis and multiple scales that may be inherent in the system dynamics being studied. This is in contrast to the usual methods of numerical analysis and computation. The technical literature is replete with numerical methods such as Runge-Kutta approach and its variations, finite element methods, and so on. However, not much attention has been given to asymptotic methods for computation, although such approaches have been widely applied with great success in the analysis of dynamic systems. The presence of differen
Yamanaka, T.; Matsuo, D.; Hirota, M.
2008-12-01
To confirm usefulness of a diagnostic model for estimating root water uptake profile by an isotopic approach, isotopic measurements of plant xylem water, soil water and groundwater were conducted at seven Japanese red pine forest sites and then the model was applied to the measured results. The model assumes that depth profile of relative uptake rate can be approximated by the normal distribution function, and xylem water isotopic composition is computed from interpolated depth profile of isotopic composition of subsurface waters. The peak depth and distribution range of water uptake zone for a given species at a given site are inversely determined by direct search method (assuming depth interval of 5 cm up to 2 m) so as to minimize root mean square error throughout observation period. Estimated water uptake profiles showed that in six sites the uptake zone of Japanese red pine (Pinus densiflora) ranged from 5 to 60 cm depth, while it was changed to deeper depths in the other site where Quercus myrsinaefolia and Pleioblastus chino coexist. On the other hand, Populus sieboldi and Malus sieboldii take up water from depths deeper than those for Pinus densiflora within a community, although the two species are usually considered as shallow rooted plants. These results indicate water source partitioning under inter-species competition, and we conclude that the present model is capable of making clear the plant water use strategy. Estimated water uptake zone also provides useful information for improving/calibrating prognostic, physical models of root water uptake.
Steinberg, Idan; Harbater, Osnat; Gannot, Israel
2014-07-01
The diffusion approximation is useful for many optical diagnostics modalities, such as near-infrared spectroscopy. However, the simple normal incidence, semi-infinite layer model may prove lacking in estimation of deep-tissue optical properties such as required for monitoring cerebral hemodynamics, especially in neonates. To answer this need, we present an analytical multilayered, oblique incidence diffusion model. Initially, the model equations are derived in vector-matrix form to facilitate fast and simple computation. Then, the spatiotemporal reflectance predicted by the model for a complex neonate head is compared with time-resolved Monte Carlo (TRMC) simulations under a wide range of physiologically feasible parameters. The high accuracy of the multilayer model is demonstrated in that the deviation from TRMC simulations is only a few percent even under the toughest conditions. We then turn to solve the inverse problem and estimate the oxygen saturation of deep brain tissues based on the temporal and spatial behaviors of the reflectance. Results indicate that temporal features of the reflectance are more sensitive to deep-layer optical parameters. The accuracy of estimation is shown to be more accurate and robust than the commonly used single-layer diffusion model. Finally, the limitations of such approaches are discussed thoroughly.
Empirical likelihood estimation of discretely sampled processes of OU type
Institute of Scientific and Technical Information of China (English)
SUN ShuGuang; ZHANG XinSheng
2009-01-01
This paper presents an empirical likelihood estimation procedure for parameters of the discretely sampled process of Ornstein-Uhlenbeck type. The proposed procedure is based on the condi-tional characteristic function, and the maximum empirical likelihood estimator is proved to be consistent and asymptotically normal. Moreover, this estimator is shown to be asymptotically efficient under some tensity parameter can be exactly recovered, and we study the maximum empirical likelihood estimator with the plug-in estimated intensity parameter. Testing procedures based on the empirical likelihood ratio statistic are developed for parameters and for estimating equations, respectively. Finally, Monte Carlo simulations are conducted to demonstrate the performance of proposed estimators.
Asymptotic freedom, asymptotic flatness and cosmology
Kiritsis, Elias
2013-01-01
Holographic RG flows in some cases are known to be related to cosmological solutions. In this paper another example of such correspondence is provided. Holographic RG flows giving rise to asymptotically-free $\\beta$-functions have been analyzed in connection with holographic models of QCD. They are shown upon Wick rotation to provide a large class of inflationary models with logarithmically soft inflaton potentials. The scalar spectral index is universal and depends only on the number of e-foldings. The ratio of tensor to scalar power depends on the single extra real parameter that defines this class of models. The Starobinsky inflationary model as well as the recently proposed models of T-inflation are members of this class. The holographic setup gives a completely new (and contrasting) view to the stability and other problems of such inflationary models.
Asymptotic expansions for the Gaussian unitary ensemble
DEFF Research Database (Denmark)
Haagerup, Uffe; Thorbjørnsen, Steen
2012-01-01
Let g : R ¿ C be a C8-function with all derivatives bounded and let trn denote the normalized trace on the n × n matrices. In Ref. 3 Ercolani and McLaughlin established asymptotic expansions of the mean value ¿{trn(g(Xn))} for a rather general class of random matrices Xn, including the Gaussian...... Unitary Ensemble (GUE). Using an analytical approach, we provide in the present paper an alternative proof of this asymptotic expansion in the GUE case. Specifically we derive for a random matrix Xn that where k is an arbitrary positive integer. Considered as mappings of g, we determine the coefficients...
The estimation of compressive strength of normal and recycled aggregate concrete
Directory of Open Access Journals (Sweden)
Janković Ksenija
2011-01-01
Full Text Available Estimation of concrete strength is an important issue in ready-mixed concrete industry, especially, in proportioning new mixtures and for the quality assurance of the concrete produced. In this article, on the basis of the existing experimental data of compressive strength of normal and recycled aggregate concrete and equation for compressive strength calculating given in Technical regulation are compared. The accuracies of prediction by experimental data obtained in laboratory as well as by EN 1992-1-1, ACI 209 and SRPS U.M1.048 are compared on the basis of the coefficient of determination. The determination of the compressive strengths by the equation described here relies on determination of type of cement and age of concrete with the constant curing temperature.
Prediction of normal values for lactate threshold estimated by gas exchange in men and women.
Davis, J A; Storer, T W; Caiozzo, V J
1997-01-01
Lactate threshold (LT) is an index of exercise capacity and can be estimated from the gas exchange consequences of a metabolic acidosis (LT(GE)). In recent years, it has emerged as a diagnostic tool in the evaluation of subjects with exercise limitation. The purpose of this study was to develop LT(GE) prediction equations on a relatively large sample of adults and to cross-validate each equation. A total of 204 healthy, sedentary, nonsmoking subjects (103 men and 101 women), aged 20-70 years, underwent graded exercise testing on a cycle ergometer. The V-slope technique was used to detect LTGE as the oxygen uptake (VO2) at the breakpoint of the carbon dioxide output versus VO2 relationship. Multiple linear regression was used to develop 12 equations with combinations of the following predictor variables: age, height, body mass, and fat-free mass. Eight of the equations are gender-specific and four are generalized with gender as a dummy variable. The equations were cross-validated using the predicted residual sum of squares (PRESS) method. The results demonstrate that the equations had relatively high multiple correlations (0.577-0.863) and low standard errors of the estimate (0.123-0.228 1 x min(-1)). The PRESS method demonstrated that the equations are generalizable, i.e., can be used in future studies without a significant loss of accuracy. Since we tested only healthy, sedentary subjects, our equations can be used to predict the lower limit of normal for a given subject. Using individual data for healthy and diseased subjects from the literature, we found that our gender-specific equations rarely miscategorized subjects unless they were obese and mass was a predictor variable. We conclude that our equations provide accurate predictions of normal values for LT(GE) and that they are generalizable to other subject populations.
Estimate of normal tissue damage in treatment planning for stereotactic radiotherapy
Energy Technology Data Exchange (ETDEWEB)
Benassi, M. (Laboratorio Fisica Medica e Sistemi Esperti, C.R.S., Ist. Regina Elena, Rome (Italy)); Begnozzi, L. (Laboratorio Fisica Medica e Sistemi Esperti, C.R.S., Ist. Regina Elena, Rome (Italy)); Gentile, F.P. (Laboratorio Fisica Medica e Sistemi Esperti, C.R.S., Ist. Regina Elena, Rome (Italy)); Chiatti, L. (Laboratorio Fisica Medica e Sistemi Esperti, C.R.S., Ist. Regina Elena, Rome (Italy)); Carpino, S. (Laboratorio Fisica Medica e Sistemi Esperti, C.R.S., Ist. Regina Elena, Rome (Italy))
1993-10-01
A personal computer (PC) system was developed to perform treatment planning for radiosurgery and stereotactic radiotherapy. These techniques of irradiation of the brain may be accomplished with a linear accelerator by performing several non-coplanar arcs of a highly collimated beam focused at a fixed point. The PC system allows the acquisition, reconstruction and the visualization of the target volume from CT or MR images, and then it permits to calculate a three-dimensional (3-D) dose distribution due to small photon beams and to visualize it. The software calculates not only total dose distribution, administered fractionated or in single fraction, but also in NTD2 (normalized total dose) predicted to have a biological effect equivalent to the single irradiation. The choice of the best technique is supported by the dose volume histograms (DVH) calculation and by an estimate of complication probability to the brain normal tissue (NTCP). The algorithm for NTCP calculation is based on two models: The linear quadratic and the logistic. A comparison of three different dose calculations for a typical cerebral target volume is presented to demonstrate the system performances. (orig.)
Konosevich, B. I.
2014-07-01
The error of the Wentzel-Kramers-Brillouin solution of the equations describing the angular motion of the axis of symmetry of rotation of a rigid body (projectile) is estimated. It is established that order of this estimate does not depend on whether the low-frequency oscillations of the axis of symmetry are damped or not
An asymptotically optimal nonparametric adaptive controller
Institute of Scientific and Technical Information of China (English)
郭雷; 谢亮亮
2000-01-01
For discrete-time nonlinear stochastic systems with unknown nonparametric structure, a kernel estimation-based nonparametric adaptive controller is constructed based on truncated certainty equivalence principle. Global stability and asymptotic optimality of the closed-loop systems are established without resorting to any external excitations.
Nanofluid surface wettability through asymptotic contact angle.
Vafaei, Saeid; Wen, Dongsheng; Borca-Tasciuc, Theodorian
2011-03-15
This investigation introduces the asymptotic contact angle as a criterion to quantify the surface wettability of nanofluids and determines the variation of solid surface tensions with nanofluid concentration and nanoparticle size. The asymptotic contact angle, which is only a function of gas-liquid-solid physical properties, is independent of droplet size for ideal surfaces and can be obtained by equating the normal component of interfacial force on an axisymmetric droplet to that of a spherical droplet. The technique is illustrated for a series of bismuth telluride nanofluids where the variation of surface wettability is measured and evaluated by asymptotic contact angles as a function of nanoparticle size, concentration, and substrate material. It is found that the variation of nanofluid concentration, nanoparticle size, and substrate modifies both the gas-liquid and solid surface tensions, which consequently affects the force balance at the triple line, the contact angle, and surface wettability.
Online Least Squares Estimation with Self-Normalized Processes: An Application to Bandit Problems
Abbasi-Yadkori, Yasin; Szepesvari, Csaba
2011-01-01
The analysis of online least squares estimation is at the heart of many stochastic sequential decision making problems. We employ tools from the self-normalized processes to provide a simple and self-contained proof of a tail bound of a vector-valued martingale. We use the bound to construct a new tighter confidence sets for the least squares estimate. We apply the confidence sets to several online decision problems, such as the multi-armed and the linearly parametrized bandit problems. The confidence sets are potentially applicable to other problems such as sleeping bandits, generalized linear bandits, and other linear control problems. We improve the regret bound of the Upper Confidence Bound (UCB) algorithm of Auer et al. (2002) and show that its regret is with high-probability a problem dependent constant. In the case of linear bandits (Dani et al., 2008), we improve the problem dependent bound in the dimension and number of time steps. Furthermore, as opposed to the previous result, we prove that our bou...
Accuracy of Cortical Evoked Response Audiometry in estimating normal hearing thresholds
Directory of Open Access Journals (Sweden)
Mahdavi M E
2007-07-01
Full Text Available Background: Cortical Evoked Response Audiometry (CERA refers to prediction of behavioral pure-tone thresholds (500-4000 Hz obtained by recording the N1-P2 complex of auditory long latency responses. CERA is the preferred method for frequency–specific estimation of audiogram in conscious adults and older children. CERA has an increased accuracy of determination of the hearing thresholds of alert patients with elevated hearing thresholds with sensory hearing loss; however few publications report studies regarding the use of CERA for estimating normal hearing thresholds. The purpose of this research was to further study the accuracy of CERA in predicting hearing thresholds when there is no hearing loss. Methods: Behavioral hearing thresholds of 40 alert normal hearing young adult male (40 ears screened at 20 dB HL in 500-8000Hz, predicted by recording N1-P2 complex of auditory evoked long latency responses to 10-30-10 ms tone bursts. After CERA, pure tone audiometry performed by other audiologist. All judgments about presence of responses performed visually. Stimulus rate variation and temporary interruption of stimulus presentation was used for preventing amplitude reduction of the responses. 200-250 responses were averaged near threshold. Results: In 95% of the hearing threshold predictions, N1-P2 thresholds were within 0-15 dB SL of true hearing thresholds. In the other 5%, the difference between the CERA threshold and true hearing threshold was 20-25 dB. The mean threshold obtained for tone bursts of 0.5, 1, 2 and 4 kHz were 12.6 ± 4.5, 10.9 ± 5.8, 10.8 ± 6.5 and 11.2 ± 4.1 dB, respectively, above the mean behavioral hearing thresholds for air-conducted pure tone stimuli. Conclusion: On average, CERA has a relatively high accuracy for the prediction of normal hearing sensitivity, comparable to that of previous studies performed on CERA in hearing-impaired populations.
Xu, Tianhua
2016-01-01
The theoretical analysis of the one-tap normalized least-mean-square carrier phase estimation (CPE) is carried out in long-haul high speed coherent optical fiber communication systems. It is found that the one-tap normalized least-mean-square equalizer shows a similar performance compared to the traditional differential detection in the carrier phase recovery.
Chen, Xiaohong; Fan, Yanqin; Pouzo, Demian; Ying, Zhiliang
2010-07-01
We study estimation and model selection of semiparametric models of multivariate survival functions for censored data, which are characterized by possibly misspecified parametric copulas and nonparametric marginal survivals. We obtain the consistency and root-n asymptotic normality of a two-step copula estimator to the pseudo-true copula parameter value according to KLIC, and provide a simple consistent estimator of its asymptotic variance, allowing for a first-step nonparametric estimation of the marginal survivals. We establish the asymptotic distribution of the penalized pseudo-likelihood ratio statistic for comparing multiple semiparametric multivariate survival functions subject to copula misspecification and general censorship. An empirical application is provided.
de Reyna, Juan Arias
2012-01-01
A new derivation of the classic asymptotic expansion of the n-th prime is presented. A fast algorithm for the computation of its terms is also given, which will be an improvement of that by Salvy (1994). Realistic bounds for the error with $\\li^{-1}(n)$, after having retained the first m terms, for $1\\le m\\le 11$, are given. Finally, assuming the Riemann Hypothesis, we give estimations of the best possible $r_3$ such that, for $n\\ge r_3$, we have $p_n> s_3(n)$ where $s_3(n)$ is the sum of the first four terms of the asymptotic expansion.
Estimating the Upcrossings Index
Sebastião, João Renato; Ferreira, Helena; Pereira, Luísa
2012-01-01
For stationary sequences, under general local and asymptotic dependence restrictions, any limiting point process for time normalized upcrossings of high levels is a compound Poisson process, i.e., there is a clustering of high upcrossings, where the underlying Poisson points represent cluster positions, and the multiplicities correspond to cluster sizes. For such classes of stationary sequences there exists the upcrossings index $\\eta,$ $0\\leq \\eta\\leq 1,$ which is directly related to the extremal index $\\theta,$ $0\\leq \\theta\\leq 1,$ for suitable high levels. In this paper we consider the problem of estimating the upcrossings index $\\eta$ for a class of stationary sequences satisfying a mild oscillation restriction. For the proposed estimator, properties such as consistency and asymptotic normality are studied. Finally, the performance of the estimator is assessed through simulation studies for autoregressive processes and case studies in the fields of environment and finance.
Peters, B. C., Jr.; Walker, H. F.
1975-01-01
New results and insights concerning a previously published iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions were discussed. It was shown that the procedure converges locally to the consistent maximum likelihood estimate as long as a specified parameter is bounded between two limits. Bound values were given to yield optimal local convergence.
Zhu, Ke; 10.1214/11-AOS895
2012-01-01
This paper investigates the asymptotic theory of the quasi-maximum exponential likelihood estimators (QMELE) for ARMA--GARCH models. Under only a fractional moment condition, the strong consistency and the asymptotic normality of the global self-weighted QMELE are obtained. Based on this self-weighted QMELE, the local QMELE is showed to be asymptotically normal for the ARMA model with GARCH (finite variance) and IGARCH errors. A formal comparison of two estimators is given for some cases. A simulation study is carried out to assess the performance of these estimators, and a real example on the world crude oil price is given.
Asymptotically hyperbolic connections
Fine, Joel; Krasnov, Kirill; Scarinci, Carlos
2015-01-01
General Relativity in 4 dimensions can be equivalently described as a dynamical theory of SO(3)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analog of the Fefferman-Graham expansion in the language of connections. As in the metric setup, one can solve the arising "evolution" equations order by order in the expansion in powers of the radial coordinate. The solution in the connection setting is arguably simpler, and very straightforward algebraic manipulations allow one to see how the obstruction appears at third order in the expansion. Another interesting feature of the connection formulation is that the "counter terms" required in the computation of the renormalised volume all combine into the Chern-Simons functional of the restriction of the connection to the boundary. As the Chern-Simons invariant is only defined modulo large gauge transformations, the requirement that the path integral over asymptotically hyperbolic connections is well-d...
DEFF Research Database (Denmark)
Litim, Daniel F.; Sannino, Francesco
2014-01-01
We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet ...... fixed points, strictly controlled by perturbation theory. Extensions towards strong coupling and beyond the large-N limit are discussed.......We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet...
Litim, Daniel F
2014-01-01
We study the ultraviolet behaviour of four-dimensional quantum field theories involving non-abelian gauge fields, fermions and scalars in the Veneziano limit. In a regime where asymptotic freedom is lost, we explain how the three types of fields cooperate to develop fully interacting ultraviolet fixed points, strictly controlled by perturbation theory. Extensions towards strong coupling and beyond the large-N limit are discussed.
Asymptotically hyperbolic connections
Fine, Joel; Herfray, Yannick; Krasnov, Kirill; Scarinci, Carlos
2016-09-01
General relativity in four-dimensions can be equivalently described as a dynamical theory of {SO}(3)˜ {SU}(2)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analogue of the Fefferman-Graham expansion in the language of connections. As in the metric setup, one can solve the arising ‘evolution’ equations order by order in the expansion in powers of the radial coordinate. The solution in the connection setting is arguably simpler, and very straightforward algebraic manipulations allow one to see how the unconstrained by Einstein equations ‘stress-energy tensor’ appears at third order in the expansion. Another interesting feature of the connection formulation is that the ‘counter terms’ required in the computation of the renormalised volume all combine into the Chern-Simons functional of the restriction of the connection to the boundary. As the Chern-Simons invariant is only defined modulo large gauge transformations, the requirement that the path integral over asymptotically hyperbolic connections is well-defined requires the cosmological constant to be quantised. Finally, in the connection setting one can deform the 4D Einstein condition in an interesting way, and we show that asymptotically hyperbolic connection expansion is universal and valid for any of the deformed theories.
Composite asymptotic expansions
Fruchard, Augustin
2013-01-01
The purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansions near turning points. Thus our approach is closely related to the method of matched asymptotic expansions. CAsEs offer two unique advantages, however. First, they provide uniform expansions near a turning point and away from it. Second, a Gevrey version of CAsEs is available and detailed in the lecture notes. Three problems are presented in which CAsEs are useful. The first application concerns canard solutions near a multiple turning point. The second application concerns so-called non-smooth or angular canard solutions. Finally an Ackerberg-O’Malley resonance pro...
Efficient Quantile Estimation for Functional-Coefficient Partially Linear Regression Models
Institute of Scientific and Technical Information of China (English)
Zhangong ZHOU; Rong JIANG; Weimin QIAN
2011-01-01
The quantile estimation methods are proposed for functional-coefficient partially linear regression (FCPLR) model by combining nonparametric and functional-coefficient regression (FCR) model.The local linear scheme and the integrated method are used to obtain local quantile estimators of all unknown functions in the FCPLR model.These resulting estimators are asymptotically normal,but each of them has big variance.To reduce variances of these quantile estimators,the one-step backfitting technique is used to obtain the efficient quantile estimators of all unknown functions,and their asymptotic normalities are derived.Two simulated examples are carried out to illustrate the proposed estimation methodology.
Jones, Douglas H.
The progress of modern mental test theory depends very much on the techniques of maximum likelihood estimation, and many popular applications make use of likelihoods induced by logistic item response models. While, in reality, item responses are nonreplicate within a single examinee and the logistic models are only ideal, practitioners make…
Energy Technology Data Exchange (ETDEWEB)
Madkour, M.A.; Hamed, A.B. [Physics Department, Faculty of Science, Mansoura University (Egypt); El-Metwally, M. [Physics Department, Faculty of Education at Suez, Suez Canal University, Suez (Egypt)
2006-03-01
The results obtained by using seven-parameterization broadband models to estimate Direct Normal Irradiance (DNI) along with two spectral models for four sites in Egypt atmosphere were compared with ground DNI measurements. Some statistical indicators (MBE, RMSE and R{sup 2}) have been used to measure the performance of the used models. MBE for all dataset is <1% to both spectral models (SPCTRAL2, SMARTS2) and broadband models (MLWT1, MLWT2 and REST) while is equal to 1.2% to YANG model. However, RMSE are around 2% for spectral models and 3% to the broadband models. The error in prediction of DNI to such models is below experimental errors a part from the big number of observations. On the other hand, Louche, Dogniaux and Rodgers models provide relatively bad performance, RMSE are at most cases >4%. Determination coefficient (R{sup 2}) results to all models are near 1.0. If we excluded spectral models, the broadband models MLWT1, MLWT2 and REST along with YANG models provide the best performance in all tests, therefore, those models can be used in Egypt atmosphere. (author)
Urrutia, Jackie D.; Tampis, Razzcelle L.; Mercado, Joseph; Baygan, Aaron Vito M.; Baccay, Edcon B.
2016-02-01
The objective of this research is to formulate a mathematical model for the Philippines' Real Gross Domestic Product (Real GDP). The following factors are considered: Consumers' Spending (x1), Government's Spending (x2), Capital Formation (x3) and Imports (x4) as the Independent Variables that can actually influence in the Real GDP in the Philippines (y). The researchers used a Normal Estimation Equation using Matrices to create the model for Real GDP and used α = 0.01.The researchers analyzed quarterly data from 1990 to 2013. The data were acquired from the National Statistical Coordination Board (NSCB) resulting to a total of 96 observations for each variable. The data have undergone a logarithmic transformation particularly the Dependent Variable (y) to satisfy all the assumptions of the Multiple Linear Regression Analysis. The mathematical model for Real GDP was formulated using Matrices through MATLAB. Based on the results, only three of the Independent Variables are significant to the Dependent Variable namely: Consumers' Spending (x1), Capital Formation (x3) and Imports (x4), hence, can actually predict Real GDP (y). The regression analysis displays that 98.7% (coefficient of determination) of the Independent Variables can actually predict the Dependent Variable. With 97.6% of the result in Paired T-Test, the Predicted Values obtained from the model showed no significant difference from the Actual Values of Real GDP. This research will be essential in appraising the forthcoming changes to aid the Government in implementing policies for the development of the economy.
Directory of Open Access Journals (Sweden)
Juliusson Gunnar
2008-10-01
Full Text Available Abstract Background Illumina Infinium whole genome genotyping (WGG arrays are increasingly being applied in cancer genomics to study gene copy number alterations and allele-specific aberrations such as loss-of-heterozygosity (LOH. Methods developed for normalization of WGG arrays have mostly focused on diploid, normal samples. However, for cancer samples genomic aberrations may confound normalization and data interpretation. Therefore, we examined the effects of the conventionally used normalization method for Illumina Infinium arrays when applied to cancer samples. Results We demonstrate an asymmetry in the detection of the two alleles for each SNP, which deleteriously influences both allelic proportions and copy number estimates. The asymmetry is caused by a remaining bias between the two dyes used in the Infinium II assay after using the normalization method in Illumina's proprietary software (BeadStudio. We propose a quantile normalization strategy for correction of this dye bias. We tested the normalization strategy using 535 individual hybridizations from 10 data sets from the analysis of cancer genomes and normal blood samples generated on Illumina Infinium II 300 k version 1 and 2, 370 k and 550 k BeadChips. We show that the proposed normalization strategy successfully removes asymmetry in estimates of both allelic proportions and copy numbers. Additionally, the normalization strategy reduces the technical variation for copy number estimates while retaining the response to copy number alterations. Conclusion The proposed normalization strategy represents a valuable tool that improves the quality of data obtained from Illumina Infinium arrays, in particular when used for LOH and copy number variation studies.
Archana V; Aruna Rao K
2014-01-01
Co-efficient of variation is a unitless measure of dispersion and is very frequently used in scientific investigations. This has motivated several researchers to propose estimators and tests concerning the co-efficient of variation of normal distribution(s). While proposing a class of estimators for the co-efficient of variation of a finite population, Tripathi et al., (2002) suggested that the estimator of co-efficient of variation of a finite population can also be used as an estimator of C...
Asymptotics for Nonlinear Transformations of Fractionally Integrated Time Series
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The asymptotic theory for nonlinear transformations of fractionally integrated time series is developed. By the use of fractional Occupation Times Formula, various nonlinear functions of fractionally integrated series such as ARFIMA time series are studied, and the asymptotic distributions of the sample moments of such functions are obtained and analyzed. The transformations considered in this paper includes a variety of functions such as regular functions, integrable functions and asymptotically homogeneous functions that are often used in practical nonlinear econometric analysis. It is shown that the asymptotic theory of nonlinear transformations of original and normalized fractionally integrated processes is different from that of fractionally integrated processes, but is similar to the asymptotic theory of nonlinear transformations of integrated processes.
Ho, Pei-Ming
2017-04-01
Following earlier works on the KMY model of black-hole formation and evaporation, we construct the metric for a matter sphere in gravitational collapse, with the back-reaction of pre-Hawking radiation taken into consideration. The mass distribution and collapsing velocity of the matter sphere are allowed to have an arbitrary radial dependence. We find that a generic gravitational collapse asymptote to a universal configuration which resembles a black hole but without horizon. This approach clarifies several misunderstandings about black-hole formation and evaporation, and provides a new model for black-hole-like objects in the universe.
Ho, Pei-Ming
2016-01-01
Following earlier works on the KMY model of black-hole formation and evaporation, we construct the metric for a matter sphere in gravitational collapse, with the back-reaction of pre-Hawking radiation taken into consideration. The mass distribution and collapsing velocity of the matter sphere are allowed to have an arbitrary radial dependence. We find that a generic gravitational collapse asymptote to a universal configuration which resembles a black hole but without horizon. This approach clarifies several misunderstandings about black-hole formation and evaporation, and provides a new model for black-hole-like objects in the universe.
Confinement versus asymptotic freedom
Dubin, A Yu
2002-01-01
I put forward the low-energy confining asymptote of the solution $$ (valid for large macroscopic contours C of the size $>>1/\\Lambda_{QCD}$) to the large N Loop equation in the D=4 U(N) Yang-Mills theory with the asymptotic freedom in the ultraviolet domain. Adapting the multiscale decomposition characteristic of the Wilsonean renormgroup, the proposed Ansatz for the loop-average is composed in order to sew, along the lines of the bootstrap approach, the large N weak-coupling series for high-momentum modes with the $N\\to{\\infty}$ limit of the recently suggested stringy representation of the 1/N strong-coupling expansion Dub4 applied to low-momentum excitations. The resulting low-energy stringy theory can be described through such superrenormalizable deformation of the noncritical Liouville string that, being devoid of ultraviolet divergences, does not possess propagating degrees of freedom at short-distance scales $<<1/{\\sqrt{\\sigma_{ph}}}$, where $\\sigma_{ph}\\sim{(\\Lambda_{QCD})^{2}}$ is the physical s...
Asymptotic Symmetries from finite boxes
Andrade, Tomas
2015-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a "box." This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the Anti-de Sitter and Poincar\\'e asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2+1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS$_3$ and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
DEFF Research Database (Denmark)
Silver, Jeremy D; Ritchie, Matthew E; Smyth, Gordon K
2009-01-01
is developed for exact maximum likelihood estimation (MLE) using high-quality optimization software and using the saddle-point estimates as starting values. "MLE" is shown to outperform heuristic estimators proposed by other authors, both in terms of estimation accuracy and in terms of performance on real data....... The saddle-point approximation is an adequate replacement in most practical situations. The performance of normexp for assessing differential expression is improved by adding a small offset to the corrected intensities....
Estimating post-fire organic soil depth in the Alaskan boreal forest using the Normalized Burn Ratio
D. Verbyla; R. Lord
2008-01-01
As part of a long-term moose browse/fire severity study, we used the Normalized Burn Ratio (NBR) with historic Landsat Thematic Mapper (TM) imagery to estimate fire severity from a 1983 wildfire in interior Alaska. Fire severity was estimated in the field by measuring the depth of the organic soil at 57 sites during the summer of 2006. Sites were selected for field...
Directory of Open Access Journals (Sweden)
Yerriswamy Wooluru
2016-06-01
Full Text Available Process capability indices are very important process quality assessment tools in automotive industries. The common process capability indices (PCIs Cp, Cpk, Cpm are widely used in practice. The use of these PCIs based on the assumption that process is in control and its output is normally distributed. In practice, normality is not always fulfilled. Indices developed based on normality assumption are very sensitive to non- normal processes. When distribution of a product quality characteristic is non-normal, Cp and Cpk indices calculated using conventional methods often lead to erroneous interpretation of process capability. In the literature, various methods have been proposed for surrogate process capability indices under non normality but few literature sources offer their comprehensive evaluation and comparison of their ability to capture true capability in non-normal situation. In this paper, five methods have been reviewed and capability evaluation is carried out for the data pertaining to resistivity of silicon wafer. The final results revealed that the Burr based percentile method is better than Clements method. Modelling of non-normal data and Box-Cox transformation method using statistical software (Minitab 14 provides reasonably good result as they are very promising methods for non - normal and moderately skewed data (Skewness <= 1.5.
Thermodynamics of Asymptotically Conical Geometries.
Cvetič, Mirjam; Gibbons, Gary W; Saleem, Zain H
2015-06-12
We study the thermodynamical properties of a class of asymptotically conical geometries known as "subtracted geometries." We derive the mass and angular momentum from the regulated Komar integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges, we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other asymptotically conical geometries.
Directory of Open Access Journals (Sweden)
Xionghua Wu
2012-01-01
Full Text Available Let {}⊂(0,1 be such that →1 as →∞, let and be two positive numbers such that +=1, and let be a contraction. If be a continuous asymptotically pseudocontractive self-mapping of a nonempty bounded closed convex subset of a real reflexive Banach space with a uniformly Gateaux differentiable norm, under suitable conditions on the sequence {}, we show the existence of a sequence {} satisfying the relation =(1−/(+(/ and prove that {} converges strongly to the fixed point of , which solves some variational inequality provided is uniformly asymptotically regular. As an application, if be an asymptotically nonexpansive self-mapping of a nonempty bounded closed convex subset of a real Banach space with a uniformly Gateaux differentiable norm and which possesses uniform normal structure, we prove that the iterative process defined by 0∈,+1=(1−/(+(/+(/ converges strongly to the fixed point of .
Sudahar, H; Kurup, P G G; Murali, V; Mahadev, P; Velmurugan, J
2012-04-01
As the α/β value of prostate is very small and lower than the surrounding critical organs, hypofractionated radiotherapy became a vital mode of treatment of prostate cancer. Cyberknife (Accuray Inc., Sunnyvale, CA, USA) treatment for localized prostate cancer is performed in hypofractionated dose regimen alone. Effective dose escalation in the hypofractionated regimen can be estimated if the corresponding conventional 2 Gy per fraction equivalent normalized total dose (NTD) distribution is known. The present study aims to analyze the hypofractionated dose distribution of localized prostate cancer in terms of equivalent NTD. Randomly selected 12 localized prostate cases treated in cyberknife with a dose regimen of 36.25 Gy in 5 fractions were considered. The 2 Gy per fraction equivalent NTDs were calculated using the formula derived from the linear quadratic (LQ) model. Dose distributions were analyzed with the corresponding NTDs. The conformity index for the prescribed target dose of 36.25 Gy equivalent to the NTD dose of 90.63 Gy (α/β = 1.5) or 74.31 Gy (α/β = 3) was ranging between 1.15 and 1.73 with a mean value of 1.32 ± 0.15. The D5% of the target was 111.41 ± 8.66 Gy for α/β = 1.5 and 90.15 ± 6.57 Gy for α/β = 3. Similarly, the D95% was 91.98 ± 3.77 Gy for α/β = 1.5 and 75.35 ± 2.88 Gy for α/β = 3. The mean values of bladder and rectal volume receiving the prescribed dose of 36.25 Gy were 0.83 cm3 and 0.086 cm3, respectively. NTD dose analysis shows an escalated dose distribution within the target for low α/β (1.5 Gy) with reasonable sparing of organs at risk. However, the higher α/β of prostate (3 Gy) is not encouraging the fact of dose escalation in cyberknife hypofractionated dose regimen of localized prostate cancer.
Afroze, Khizer Hussain; Prabha, Subhash Lakshmi; Chandrakala, V; Deepak, M
2017-08-01
The routine antenatal sonographic investigations of the umbilical cord are limited for assessment of number of umbilical vessels and doppler evaluation of umbilical blood flow. With the advancements of the sonographic techniques it is now possible to have more detailed evaluation of umbilical cord. There exist only few literatures on assessment of umbilical cord cross-sectional area during pregnancy to provide a baseline reference value. To establish the reference intervals of cross-sectional area of the umbilical cord during gestation and to find the correlation of umbilical cord cross-sectional area with the foetal anthropometric measurements. This study was conducted among 214 normal pregnant women who underwent a routine antenatal sonogram during gestational age ranging from 24-39 weeks in the Department of Radiodiagnosis. The umbilical cord cross-sectional area was calculated at a plane immediately close to the umbilical cord insertion to the foetal abdomen. The following foetal parameters were studied: Biparietal Diameters (BPD), Head Circumference (HC), Abdominal Circumference (AC), Femur Length (FL), and Estimated Foetal weight (EFW). The relationship between foetal anthropometric measurements and umbilical cord cross sectional area was assessed using spearman rank correlation. The 5(th), 10(th), 50(th), 90(th) and 95(th) percentiles of umbilical cord cross-sectional area were calculated for each gestational groups using polynomial regression analysis. A statistically significant correlation was observed between cross-sectional area of umbilical cord with both gestational age and foetal anthropometric parameters. The mean age of study population was 25.08±3.5 years and the mean gestational age was 34.42±2.5 weeks. We observed a strong correlation between head circumference and umbilical cord cross-sectional area. The mean umbilical cord cross-section area increases steadily with gestational age for up to 34 weeks and then it declines. Umbilical cord cross
Asymptotically safe grand unification
Bajc, Borut; Sannino, Francesco
2016-12-01
Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.
Asymptotically Safe Grand Unification
Bajc, Borut
2016-01-01
Phenomenologically appealing supersymmetric grand unified theories have large gauge representations and thus are not asymptotically free. Their ultraviolet validity is limited by the appearance of a Landau pole well before the Planck scale. One could hope that these theories save themselves, before the inclusion of gravity, by generating an interacting ultraviolet fixed point, similar to the one recently discovered in non-supersymmetric gauge-Yukawa theories. Employing a-maximization, a-theorem, unitarity bounds, as well as positivity of other central charges we nonperturbatively rule out this possibility for a broad class of prime candidates of phenomenologically relevant supersymmetric grand unified theories. We also uncover candidates passing these tests, which have either exotic matter or contain one field decoupled from the superpotential. The latter class of theories contains a model with the minimal matter content required by phenomenology.
asymptoticMK: A Web-Based Tool for the Asymptotic McDonald-Kreitman Test.
Haller, Benjamin C; Messer, Philipp W
2017-03-24
The McDonald-Kreitman (MK) test is a widely used method for quantifying the role of positive selection in molecular evolution. One key shortcoming of this test lies in its sensitivity to the presence of slightly deleterious mutations, which can severely bias its estimates. An asymptotic version of the MK test was recently introduced that addresses this problem by evaluating polymorphism levels for different mutation frequencies separately, and then extrapolating a function fitted to that data. Here we present asymptoticMK, a web-based implementation of this asymptotic McDonald-Kreitman test. Our web service provides a simple R-based interface into which the user can upload the required data (polymorphism and divergence data for the genomic test region and a neutrally evolving reference region). The web service then analyzes the data and provides plots of the test results. This service is free to use, open-source, and available at http://benhaller.com/messerlab/asymptoticMK.html. We provide results from simulations to illustrate the performance and robustness of the asymptoticMK test under a wide range of model parameters.
Institute of Scientific and Technical Information of China (English)
张玲霞; 师义民
2000-01-01
Consider the two-sided truncation distribution families written in the form f(x｜θ)= ω ( θ1, θ2) h (x) I[θ1,θ2] (x), where θ= ( θ1, θ2 ) T (x) = (t1 (x), t2 (x)) = ( min (x1,…, xm ), max (x1,… ,xm)) is a sufficient statistic, its marginal density is denoted by f(t). In this paper, by estimating f(t), we construct the empirical Bayes estimation (EBE) for parameter-function Q(θ), and prove the EBE is an asymptotically optimal that of Q(θ).%本文考虑一维双边截断型分布族参数函数在平方损失下的经验 Bayes 估计问题．给定θ，x的条件分布为 f(x｜θ)=ω(θ1，θ2)h(x)I[θ1,θ2](x)dx其中 θ=(θ1，θ2) T(x)=(t1(x)，t2(x))=(min(x1，…，xm)，max(x1，…，xm))是充分统计量．其边缘密度为f(t)，本文通过f(t)的核估计构造出θ的函数的经验 Bayes 估计，并证明在一定的条件下是渐近最优的(a．0．)．
Estimating Subglottal Pressure from Neck-Surface Acceleration during Normal Voice Production
Fryd, Amanda S.; Van Stan, Jarrad H.; Hillman, Robert E.; Mehta, Daryush D.
2016-01-01
Purpose: The purpose of this study was to evaluate the potential for estimating subglottal air pressure using a neck-surface accelerometer and to compare the accuracy of predicting subglottal air pressure relative to predicting acoustic sound pressure level (SPL). Method: Indirect estimates of subglottal pressure (P[subscript sg]') were obtained…
二维递归序列的渐近性%Asymptotics on Two-dimensional Recursion Sequences
Institute of Scientific and Technical Information of China (English)
乌云高娃; 王天明
2007-01-01
In this paper, we give precise formulas for the general two-dimensional recursion sequences by generating function method, and make use of the multivariate generating functions asymptotic estimation technique to compute their asymptotic values.
Adaptive quasi-likelihood estimate in generalized linear models
Institute of Scientific and Technical Information of China (English)
CHEN Xia; CHEN Xiru
2005-01-01
This paper gives a thorough theoretical treatment on the adaptive quasilikelihood estimate of the parameters in the generalized linear models. The unknown covariance matrix of the response variable is estimated by the sample. It is shown that the adaptive estimator defined in this paper is asymptotically most efficient in the sense that it is asymptotic normal, and the covariance matrix of the limit distribution coincides with the one for the quasi-likelihood estimator for the case that the covariance matrix of the response variable is completely known.
Uniform Asymptotic Expansion for the Incomplete Beta Function
Nemes, Gergő; Olde Daalhuis, Adri B.
2016-10-01
In [Temme N.M., Special functions. An introduction to the classical functions of mathematical physics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, Section 11.3.3.1] a uniform asymptotic expansion for the incomplete beta function was derived. It was not obvious from those results that the expansion is actually an asymptotic expansion. We derive a remainder estimate that clearly shows that the result indeed has an asymptotic property, and we also give a recurrence relation for the coefficients.
Two-step estimation for inhomogeneous spatial point processes
DEFF Research Database (Denmark)
Waagepetersen, Rasmus; Guan, Yongtao
This paper is concerned with parameter estimation for inhomogeneous spatial point processes with a regression model for the intensity function and tractable second order properties (K-function). Regression parameters are estimated using a Poisson likelihood score estimating function and in a second...... step minimum contrast estimation is applied for the residual clustering parameters. Asymptotic normality of parameter estimates is established under certain mixing conditions and we exemplify how the results may be applied in ecological studies of rain forests....
Institute of Scientific and Technical Information of China (English)
吴启光; 杨国庆
2002-01-01
In this paper, we study the existence of the uniformly minimum risk equivariant (UMRE) estimators of parameters in a class of normal linear models, which include the normal variance components model,the growth curve model, the extended growth curve model, and the seemingly unrelated regression equations model, and so on. The necessary and sufficient conditions are given for the existence of UMRE estimators of the estimable linear functions of regression coefficients, the covariance matrix V and (trV)a, where a＞ 0is known, in the models under an affine group of transformations for quadratic losses and matrix losses, respectively. Under the (extended) growth curve model and the seemingly unrelated regression equations model,the conclusions given in literature for estimating regression coefficients can be derived by applying the general results in this paper, and the sufficient conditions for non-existence of UMRE estimators of V and tr(V) are expanded to be necessary and sufficient conditions. In addition, the necessary and sufficient conditions that there exist UMRE estimators of parameters in the variance components model are obtained for the first time.
DEFF Research Database (Denmark)
Varneskov, Rasmus T.
of symmetric matrices ensures positive (semi-)definiteness without altering asymptotic properties of the class of estimators. The finite sample correction admits non-linear transformations of the estimated covariance matrix such as correlations and realized betas, and it can be used in portfolio optimization...... dependence and to be correlated with the efficient price process. Estimators in this class are shown to posses desirable statistical properties such as consistency, asymptotic normality, and asymptotic unbiasedness at an optimal n^(1/4)-convergence rate. A finite sample correction based on projections...
Directory of Open Access Journals (Sweden)
Jizheng Yi
Full Text Available Illumination normalization of face image for face recognition and facial expression recognition is one of the most frequent and difficult problems in image processing. In order to obtain a face image with normal illumination, our method firstly divides the input face image into sixteen local regions and calculates the edge level percentage in each of them. Secondly, three local regions, which meet the requirements of lower complexity and larger average gray value, are selected to calculate the final illuminant direction according to the error function between the measured intensity and the calculated intensity, and the constraint function for an infinite light source model. After knowing the final illuminant direction of the input face image, the Retinex algorithm is improved from two aspects: (1 we optimize the surround function; (2 we intercept the values in both ends of histogram of face image, determine the range of gray levels, and stretch the range of gray levels into the dynamic range of display device. Finally, we achieve illumination normalization and get the final face image. Unlike previous illumination normalization approaches, the method proposed in this paper does not require any training step or any knowledge of 3D face and reflective surface model. The experimental results using extended Yale face database B and CMU-PIE show that our method achieves better normalization effect comparing with the existing techniques.
Estimation of Partially Specified Spatial Panel Data Models with Random-Eff ects
Institute of Scientific and Technical Information of China (English)
Yuan Qing ZHANG; Guang Ren YANG
2015-01-01
In this article, we study estimation of a partially specified spatial panel data linear regres-sion with random-eff ects. Under the conditions of exogenous spatial weighting matrix and exogenous regressors, we give an instrumental variable estimation. Under certain suﬃ cient assumptions, we show that the proposed estimator for the finite dimensional parameter is root-N consistent and asymptot-ically normally distributed and the proposed estimator for the unknown function is consistent and asymptotically distributed. Consistent estimators for the asymptotic variance-covariance matrices of both the parametric and unknown components are provided. The Monte Carlo simulation results verify our theory and suggest that the approach has some practical value.
ESTIMATING HAZARD RATIOS IN NESTED CASE-CONTROL STUDIES BY MANTEL-HAENSZEL METHOD
Institute of Scientific and Technical Information of China (English)
张忠占
2001-01-01
In this article, a class of Mantel-Haenszel type estimators of hazard ratios in proportional hazards model is presented for simple nested case-control study. The estimators have the form of the Mantel-Haenszel estimator of odds ratios, and it is shown that the estimators are dually consistent, and asymptotically normal. Dually consistently estimated covariance matrices of the proposed estimators are also developed. An example is given to illustrate the estimators.
Bachour, Dunia Antoine; Fernández Sánchez, Enrique
2015-01-01
La medición precisa de la Irradiancia Directa Normal (DNI) es esencial para el diseño e implementación de proyectos CSP (energía solar concentrada). Qatar cuenta con abundante radiación solar; por lo tanto, el aprovechamiento de la misma es de gran interés en esta región, en particular para sistemas de concentración solar. Antes de embarcarse en dichos proyectos, se debe contar con datos de irradiancia directa normal confiables y de buena calidad. Actualmente, los mapas existentes de radiació...
Bachour, Dunia Antoine
2015-01-01
La medición precisa de la Irradiancia Directa Normal (DNI) es esencial para el diseño e implementación de proyectos CSP (energía solar concentrada). Qatar cuenta con abundante radiación solar; por lo tanto, el aprovechamiento de la misma es de gran interés en esta región, en particular para sistemas de concentración solar. Antes de embarcarse en dichos proyectos, se debe contar con datos de irradiancia directa normal confiables y de buena calidad. Actualmente, los mapas existen...
An asymptotically exact theory of functionally graded piezoelectric shells
Le, Khanh Chau
2016-01-01
An asymptotically exact two-dimensional theory of functionally graded piezoelectric shells is derived by the variational-asymptotic method. The error estimation of the constructed theory is given in the energetic norm. As an application, analytical solution to the problem of forced vibration of a functionally graded piezoceramic cylindrical shell with thickness polarization fully covered by electrodes and excited by a harmonic voltage is found.
An asymptotically exact theory of smart sandwich shells
Le, Khanh Chau
2016-01-01
An asymptotically exact two-dimensional theory of elastic-piezoceramic sandwich shells is derived by the variational-asymptotic method. The error estimation of the constructed theory is given in the energetic norm. As an application, analytical solution to the problem of forced vibration of a circular elastic plate partially covered by two piezoceramic patches with thickness polarization excited by a harmonic voltage is found.
Asymptotic behaviour for a diffusion equation governed by nonlocal interactions
Ovono, Armel Andami
2010-01-01
In this paper we study the asymptotic behaviour of a nonlocal nonlinear parabolic equation governed by a parameter. After giving the existence of unique branch of solutions composed by stable solutions in stationary case, we gives for the parabolic problem $L^\\infty $ estimates of solution based on using the Moser iterations and existence of global attractor. We finish our study by the issue of asymptotic behaviour in some cases when $t\\to \\infty$.
Ultraviolet asymptotics of glueball propagators
Bochicchio, M
2013-01-01
We point out that perturbation theory in conjunction with the renormalization group (RG) puts a severe constraint on the structure of the large-N non-perturbative glueball propagators in SU(N) pure YM, in QCD and in n=1 SUSY QCD with massless quarks, or in any confining asymptotically-free gauge theory massless in perturbation theory. For the scalar and pseudoscalar glueball propagators in pure YM and QCD with massless quarks we check in detail the RG-improved estimate to the order of the leading and next-to-leading logarithms by means of a remarkable three-loop computation by Chetyrkin et al. We investigate as to whether the aforementioned constraint is satisfied by any of the scalar or pseudoscalar glueball propagators computed in the framework of the AdS String/ large-N Gauge Theory correspondence and of a recent proposal based on a Topological Field Theory underlying the large-N limit of YM. We find that none of the proposals for the scalar or the pseudoscalar glueball propagators based on the AdS String/...
The Distribution of the Product Explains Normal Theory Mediation Confidence Interval Estimation.
Kisbu-Sakarya, Yasemin; MacKinnon, David P; Miočević, Milica
2014-05-01
The distribution of the product has several useful applications. One of these applications is its use to form confidence intervals for the indirect effect as the product of 2 regression coefficients. The purpose of this article is to investigate how the moments of the distribution of the product explain normal theory mediation confidence interval coverage and imbalance. Values of the critical ratio for each random variable are used to demonstrate how the moments of the distribution of the product change across values of the critical ratio observed in research studies. Results of the simulation study showed that as skewness in absolute value increases, coverage decreases. And as skewness in absolute value and kurtosis increases, imbalance increases. The difference between testing the significance of the indirect effect using the normal theory versus the asymmetric distribution of the product is further illustrated with a real data example. This article is the first study to show the direct link between the distribution of the product and indirect effect confidence intervals and clarifies the results of previous simulation studies by showing why normal theory confidence intervals for indirect effects are often less accurate than those obtained from the asymmetric distribution of the product or from resampling methods.
Normalization Ridge Regression in Practice II: The Estimation of Multiple Feedback Linkages.
Bulcock, J. W.
The use of the two-stage least squares (2 SLS) procedure for estimating nonrecursive social science models is often impractical when multiple feedback linkages are required. This is because 2 SLS is extremely sensitive to multicollinearity. The standard statistical solution to the multicollinearity problem is a biased, variance reduced procedure…
Wang, Jingjing; Redmond, Stephen J; Voleno, Matteo; Narayanan, Michael R; Wang, Ning; Cerutti, Sergio; Lovell, Nigel H
2012-11-01
Energy expenditure (EE) is an important parameter in the assessment of physical activity. Most reliable techniques for EE estimation are too impractical for deployment in unsupervised free-living environments; those which do prove practical for unsupervised use often poorly estimate EE when the subject is working to change their altitude by walking up or down stairs or inclines. This study evaluates the augmentation of a standard triaxial accelerometry waist-worn wearable sensor with a barometric pressure sensor (as a surrogate measure for altitude) to improve EE estimates, particularly when the subject is ascending or descending stairs. Using a number of features extracted from the accelerometry and barometric pressure signals, a state space model is trained for EE estimation. An activity classification algorithm is also presented, and this activity classification output is also investigated as a model input parameter when estimating EE. This EE estimation model is compared against a similar model which solely utilizes accelerometry-derived features. A protocol (comprising lying, sitting, standing, walking, walking up stairs, walking down stairs and transitioning between activities) was performed by 13 healthy volunteers (8 males and 5 females; age: 23.8 ± 3.7 years; weight: 70.5 ± 14.9 kg), whose instantaneous oxygen uptake was measured by means of an indirect calorimetry system (K4b(2), COSMED, Italy). Activity classification improves from 81.65% to 90.91% when including barometric pressure information; when analyzing walking activities alone the accuracy increases from 70.23% to 98.54%. Using features derived from both accelerometry and barometry signals, combined with features relating to the activity classification in a state space model, resulted in a VO(2) estimation bias of -0.00 095 and precision (1.96SD) of 3.54 ml min(-1) kg(-1). Using only accelerometry features gives a relatively worse performance, with a bias of -0.09 and precision (1.96SD) of 5
Asymptotic Distribution of Coefficients of Skewness and Kurtosis
Directory of Open Access Journals (Sweden)
Narges Abbasi
2009-01-01
Full Text Available Problem statement: In literature, a classic method which has been used to recognize the distribution so far is the measurement of its skewedness and kurtosis. However, there remains a question: how would these measurements work for skewed normal distribution when the size of the sample is large? Approach: This research aimed to determine the asymptotic distribution of skewedness and kurtosis measures in skewed normal distribution. In conducting this research, two groups of inferential findings will help. First, skewed normal distribution which has already been studied by a lot of researchers and we apply its characteristics. Second, there is the U-statistics theory which guides us to the determining of asymptotic distribution measures for skewedness and kurtosis. The combination of these two will solve the problem of this study. Results: Asymptotic distribution of measures for skewdness and kurtosis falls in the normal families. With the size of large samples, the values of expectation of these measures are also determined. By letting zero for skewedness parameter, asymptotic distribution for normal distribution can also be obtained. Conclusion: The findings of this study show new characteristics for skew normal distribution and this results in a new way for skew normal distribution recognition.
Estimating developmental states of tumors and normal tissues using a linear time-ordered model
Directory of Open Access Journals (Sweden)
Xuan Zhenyu
2011-02-01
Full Text Available Abstract Background Tumor cells are considered to have an aberrant cell state, and some evidence indicates different development states appearing in the tumorigenesis. Embryonic development and stem cell differentiation are ordered processes in which the sequence of events over time is highly conserved. The "cancer attractor" concept integrates normal developmental processes and tumorigenesis into a high-dimensional "cell state space", and provides a reasonable explanation of the relationship between these two biological processes from theoretical viewpoint. However, it is hard to describe such relationship by using existed experimental data; moreover, the measurement of different development states is also difficult. Results Here, by applying a novel time-ordered linear model based on a co-bisector which represents the joint direction of a series of vectors, we described the trajectories of development process by a line and showed different developmental states of tumor cells from developmental timescale perspective in a cell state space. This model was used to transform time-course developmental expression profiles of human ESCs, normal mouse liver, ovary and lung tissue into "cell developmental state lines". Then these cell state lines were applied to observe the developmental states of different tumors and their corresponding normal samples. Mouse liver and ovarian tumors showed different similarity to early development stage. Similarly, human glioma cells and ovarian tumors became developmentally "younger". Conclusions The time-ordered linear model captured linear projected development trajectories in a cell state space. Meanwhile it also reflected the change tendency of gene expression over time from the developmental timescale perspective, and our finding indicated different development states during tumorigenesis processes in different tissues.
Risk estimation based on mixed normal distribution model for diabetes-related hospitalization claims
Institute of Scientific and Technical Information of China (English)
WANG Xin-wang; WANG Juan; FANG Ji-qian
2006-01-01
@@ Medical insurance service, the important part of national healthcare supporting system with a history dating back more than 100 years ago,remains a global challenge because of its high rates of compensation and difficulty in risk control. When developing the diabetes related, hospitalization insurance, we found that the risk loss of the diabetic inpatients does not follow a symmetrical unimodal distribution: in fact, it is hard to describe its risk loses distribution with a single probability distribution model. Therefore, we put forward a risk measurement method based on a mixed normal distributions model for medical insurance of inpatients with diabetes.
DEFF Research Database (Denmark)
Franco, Antonio; Trapp, Stefan
2008-01-01
The sorption of organic electrolytes to soil was investigated. A dataset consisting of 164 electrolytes, composed of 93 acids, 65 bases, and six amphoters, was collected from literature and databases. The partition coefficient log KOW of the neutral molecule and the dissociation constant pKa were...... calculated by the software ACD/Labs®. The Henderson-Hasselbalch equation was applied to calculate dissociation. Regressions were developed to predict separately for the neutral and the ionic molecule species the distribution coefficient (Kd) normalized to organic carbon (KOC) from log KOW and pKa. The log...
A Note on Asymptotic Contractions
Directory of Open Access Journals (Sweden)
Marina Arav
2006-12-01
Full Text Available We provide sufficient conditions for the iterates of an asymptotic contraction on a complete metric space X to converge to its unique fixed point, uniformly on each bounded subset of X.
A Note on Asymptotic Contractions
Directory of Open Access Journals (Sweden)
Castillo Santos Francisco Eduardo
2007-01-01
Full Text Available We provide sufficient conditions for the iterates of an asymptotic contraction on a complete metric space to converge to its unique fixed point, uniformly on each bounded subset of .
Asymptotic Dynamics of Monopole Walls
Cross, R
2015-01-01
We determine the asymptotic dynamics of the U(N) doubly periodic BPS monopole in Yang-Mills-Higgs theory, called a monopole wall, by exploring its Higgs curve using the Newton polytope and amoeba. In particular, we show that the monopole wall splits into subwalls when any of its moduli become large. The long-distance gauge and Higgs field interactions of these subwalls are abelian, allowing us to derive an asymptotic metric for the monopole wall moduli space.
Estimation and variable selection for generalized additive partial linear models
Wang, Li
2011-08-01
We study generalized additive partial linear models, proposing the use of polynomial spline smoothing for estimation of nonparametric functions, and deriving quasi-likelihood based estimators for the linear parameters. We establish asymptotic normality for the estimators of the parametric components. The procedure avoids solving large systems of equations as in kernel-based procedures and thus results in gains in computational simplicity. We further develop a class of variable selection procedures for the linear parameters by employing a nonconcave penalized quasi-likelihood, which is shown to have an asymptotic oracle property. Monte Carlo simulations and an empirical example are presented for illustration. © Institute of Mathematical Statistics, 2011.
Local polynomial Whittle estimation of perturbed fractional processes
DEFF Research Database (Denmark)
Frederiksen, Per; Nielsen, Frank; Nielsen, Morten Ørregaard
for d ε (0, 3/4), and if the spectral density is infinitely smooth near frequency zero, the rate of convergence can become arbitrarily close to the parametric rate, pn. A Monte Carlo study reveals that the LPWN estimator performs well in the presence of a serially correlated perturbation term...... of the signal by two separate polynomials. Including these polynomials we obtain a reduction in the order of magnitude of the bias, but also in‡ate the asymptotic variance of the long memory estimate by a multiplicative constant. We show that the estimator is consistent for d 2 (0; 1), asymptotically normal...
Energy efficiency estimation of a steam powered LNG tanker using normal operating data
Directory of Open Access Journals (Sweden)
Sinha Rajendra Prasad
2016-01-01
Full Text Available A ship’s energy efficiency performance is generally estimated by conducting special sea trials of few hours under very controlled environmental conditions of calm sea, standard draft and optimum trim. This indicator is then used as the benchmark for future reference of the ship’s Energy Efficiency Performance (EEP. In practice, however, for greater part of operating life the ship operates in conditions which are far removed from original sea trial conditions and therefore comparing energy performance with benchmark performance indicator is not truly valid. In such situations a higher fuel consumption reading from the ship fuel meter may not be a true indicator of poor machinery performance or dirty underwater hull. Most likely, the reasons for higher fuel consumption may lie in factors other than the condition of hull and machinery, such as head wind, current, low load operations or incorrect trim [1]. Thus a better and more accurate approach to determine energy efficiency of the ship attributable only to main machinery and underwater hull condition will be to filter out the influence of all spurious and non-standard operating conditions from the ship’s fuel consumption [2]. The author in this paper identifies parameters of a suitable filter to be used on the daily report data of a typical LNG tanker of 33000 kW shaft power to remove effects of spurious and non-standard ship operations on its fuel consumption. The filtered daily report data has been then used to estimate actual fuel efficiency of the ship and compared with the sea trials benchmark performance. Results obtained using data filter show closer agreement with the benchmark EEP than obtained from the monthly mini trials . The data filtering method proposed in this paper has the advantage of using the actual operational data of the ship and thus saving cost of conducting special sea trials to estimate ship EEP. The agreement between estimated results and special sea trials EEP is
DEM-Based SAR Pixel Area Estimation For Enhanced Geocoding Refinement And Radiometric Normalization
Frey, Othmar; Santoro, Maurizio; Werner, Charles L.; Wegmuller, Urs
2012-01-01
Precise terrain-corrected georeferencing of SAR images and derived products in range-Doppler coordinates is important with respect to several aspects, such as data interpretation, combination with other geodata products, and transformation of, e.g., terrain heights into SAR geometry as used in DInSAR applications. For georeferencing a look-up table is calculated and refined based on a coregistration of the actual SAR image to a simulated SAR image. The impact of using two different implementations of such a simulator of topography-induced radar brightness, an approach based on angular relationships and a pixel-area based method are discussed in this paper. It is found that the pixel-area-based method leads to considerable improvements with regard to the robustness of georeferencing and also with regard to radiometric normalization in layover- affected areas.
Concentrations of proanthocyanidins in common foods and estimations of normal consumption.
Gu, Liwei; Kelm, Mark A; Hammerstone, John F; Beecher, Gary; Holden, Joanne; Haytowitz, David; Gebhardt, Susan; Prior, Ronald L
2004-03-01
Proanthocyanidins (PAs) have been shown to have potential health benefits. However, no data exist concerning their dietary intake. Therefore, PAs in common and infant foods from the U.S. were analyzed. On the bases of our data and those from the USDA's Continuing Survey of Food Intakes by Individuals (CSFII) of 1994-1996, the mean daily intake of PAs in the U.S. population (>2 y old) was estimated to be 57.7 mg/person. Monomers, dimers, trimers, and those above trimers contribute 7.1, 11.2, 7.8, and 73.9% of total PAs, respectively. The major sources of PAs in the American diet are apples (32.0%), followed by chocolate (17.9%) and grapes (17.8%). The 2- to 5-y-old age group (68.2 mg/person) and men >60 y old (70.8 mg/person) consume more PAs daily than other groups because they consume more fruit. The daily intake of PAs for 4- to 6-mo-old and 6- to 10-mo-old infants was estimated to be 1.3 mg and 26.9 mg, respectively, based on the recommendations of the American Academy of Pediatrics. This study supports the concept that PAs account for a major fraction of the total flavonoids ingested in Western diets.
Peters, B. C., Jr.; Walker, H. F.
1976-01-01
The problem of obtaining numerically maximum likelihood estimates of the parameters for a mixture of normal distributions is addressed. In recent literature, a certain successive approximations procedure, based on the likelihood equations, is shown empirically to be effective in numerically approximating such maximum-likelihood estimates; however, the reliability of this procedure was not established theoretically. Here, a general iterative procedure is introduced, of the generalized steepest-ascent (deflected-gradient) type, which is just the procedure known in the literature when the step-size is taken to be 1. With probability 1 as the sample size grows large, it is shown that this procedure converges locally to the strongly consistent maximum-likelihood estimate whenever the step-size lies between 0 and 2. The step-size which yields optimal local convergence rates for large samples is determined in a sense by the separation of the component normal densities and is bounded below by a number between 1 and 2.
Peters, B. C., Jr.; Walker, H. F.
1978-01-01
This paper addresses the problem of obtaining numerically maximum-likelihood estimates of the parameters for a mixture of normal distributions. In recent literature, a certain successive-approximations procedure, based on the likelihood equations, was shown empirically to be effective in numerically approximating such maximum-likelihood estimates; however, the reliability of this procedure was not established theoretically. Here, we introduce a general iterative procedure, of the generalized steepest-ascent (deflected-gradient) type, which is just the procedure known in the literature when the step-size is taken to be 1. We show that, with probability 1 as the sample size grows large, this procedure converges locally to the strongly consistent maximum-likelihood estimate whenever the step-size lies between 0 and 2. We also show that the step-size which yields optimal local convergence rates for large samples is determined in a sense by the 'separation' of the component normal densities and is bounded below by a number between 1 and 2.
Testing monotonicity of a hazard: asymptotic distribution theory
Groeneboom, Piet
2011-01-01
Two new test statistics are introduced to test the null hypotheses that the sampling distribution has an increasing hazard rate on a specified interval [0,a]. These statistics are empirical L_1-type distances between the isotonic estimates, which use the monotonicity constraint, and either the empirical distribution function or the empirical cumulative hazard. They measure the excursions of the empirical estimates with respect to the isotonic estimates, due to local non-monotonicity. Asymptotic normality of the test statistics, if the hazard is strictly increasing on [0,a], is established under mild conditions. This is done by first approximating the global empirical distance by an distance with respect to the underlying distribution function. The resulting integral is treated as sum of increasingly many local integrals to which a CLT can be applied. The behavior of the local integrals is determined by a canonical process: the difference between the stochastic process x -> W(x)+x^2 where W is standard two-sid...
Polynomial Asymptotes of the Second Kind
Dobbs, David E.
2011-01-01
This note uses the analytic notion of asymptotic functions to study when a function is asymptotic to a polynomial function. Along with associated existence and uniqueness results, this kind of asymptotic behaviour is related to the type of asymptote that was recently defined in a more geometric way. Applications are given to rational functions and…
Exact, time-independent estimation of clone size distributions in normal and mutated cells.
Roshan, A; Jones, P H; Greenman, C D
2014-10-06
Biological tools such as genetic lineage tracing, three-dimensional confocal microscopy and next-generation DNA sequencing are providing new ways to quantify the distribution of clones of normal and mutated cells. Understanding population-wide clone size distributions in vivo is complicated by multiple cell types within observed tissues, and overlapping birth and death processes. This has led to the increased need for mathematically informed models to understand their biological significance. Standard approaches usually require knowledge of clonal age. We show that modelling on clone size independent of time is an alternative method that offers certain analytical advantages; it can help parametrize these models, and obtain distributions for counts of mutated or proliferating cells, for example. When applied to a general birth-death process common in epithelial progenitors, this takes the form of a gambler's ruin problem, the solution of which relates to counting Motzkin lattice paths. Applying this approach to mutational processes, alternative, exact, formulations of classic Luria-Delbrück-type problems emerge. This approach can be extended beyond neutral models of mutant clonal evolution. Applications of these approaches are twofold. First, we resolve the probability of progenitor cells generating proliferating or differentiating progeny in clonal lineage tracing experiments in vivo or cell culture assays where clone age is not known. Second, we model mutation frequency distributions that deep sequencing of subclonal samples produce.
de Almeida, Maurício Liberal; Saatkamp, Cassiano Junior; Fernandes, Adriana Barrinha; Pinheiro, Antonio Luiz Barbosa; Silveira, Landulfo
2016-09-01
Urea and creatinine are commonly used as biomarkers of renal function. Abnormal concentrations of these biomarkers are indicative of pathological processes such as renal failure. This study aimed to develop a model based on Raman spectroscopy to estimate the concentration values of urea and creatinine in human serum. Blood sera from 55 clinically normal subjects and 47 patients with chronic kidney disease undergoing dialysis were collected, and concentrations of urea and creatinine were determined by spectrophotometric methods. A Raman spectrum was obtained with a high-resolution dispersive Raman spectrometer (830 nm). A spectral model was developed based on partial least squares (PLS), where the concentrations of urea and creatinine were correlated with the Raman features. Principal components analysis (PCA) was used to discriminate dialysis patients from normal subjects. The PLS model showed r = 0.97 and r = 0.93 for urea and creatinine, respectively. The root mean square errors of cross-validation (RMSECV) for the model were 17.6 and 1.94 mg/dL, respectively. PCA showed high discrimination between dialysis and normality (95 % accuracy). The Raman technique was able to determine the concentrations with low error and to discriminate dialysis from normal subjects, consistent with a rapid and low-cost test.
ESTIMATION OF SERUM URIC ACID LEVELS IN NORMAL PREDIABETIC AND DIABETIC PERSON
Directory of Open Access Journals (Sweden)
Prakash Gurupad Mantur
2017-04-01
Full Text Available BACKGROUND Raised serum uric acid has been associated with a lot of diseases like hypertension, cardiovascular diseases, chronic kidney disease, peripheral vascular diseases and metabolic disorders. But, the association of serum uric acid levels to that of diabetes mellitus has not been successfully understood. A sincere effort has been put in this study to find out the serum uric acid levels in normal individuals, prediabetics and diabetics and come to a conclusion on the correlation of serum uric acid in diabetes mellitus. MATERIALS AND METHODS One hundred eighty people who visited the Department of Medicine were selected. The study included ninety males and ninety females and in each group there were thirty non-diabetic, thirty prediabetics and thirty diabetics. Prediabetics were considered as 110 to 125 mg/dL (6.1 mM/L to 6.9 mM/L - that is WHO criteria was followed. All the subjects were aged between 40-60 years. The correlations were made between the serum uric acid levels and serum fasting glucose, serum postprandial and HbA1c. RESULTS The results show a rise in the serum uric acid levels in the prediabetic and not so much in the non-diabetics and the confirmed diabetics. CONCLUSION The serum uric acid level measurements can be used as a powerful tool in identifying the prediabetic condition and help an individual to make the necessary lifestyle adjustments so that the progression of the diseases can be stopped or maybe infinitely delayed.
Energy Technology Data Exchange (ETDEWEB)
McCleskey, M; Mukhamedzhanov, A M; Trache, L; Tribble, R E; Banu, A; Eremenko, V; Goldberg, V Z; Lui, Y W; McCleskey, E; Roeder, B T; Spiridon, A; Carstoiu, F; Burjan, V; Hons, Z; Thompson, I J
2014-04-17
The ^{14}C + n <--> ^{15}C system has been used as a test case in the evaluation of a new method to determine spectroscopic factors that uses the asymptotic normalization coefficient (ANC). The method proved to be unsuccessful for this case. As part of this experimental program, the ANCs for the ^{15}C ground state and first excited state were determined using a heavy-ion neutron transfer reaction as well as the inverse kinematics (d,p) reaction, measured at the Texas A&M Cyclotron Institute. The ANCs were used to evaluate the astrophysical direct neutron capture rate on ^{14}C, which was then compared with the most recent direct measurement and found to be in good agreement. A study of the ^{15}C SF via its mirror nucleus ^{15}F and a new insight into deuteron stripping theory are also presented.
Estimating Recovery Failure Probabilities in Off-normal Situations from Full-Scope Simulator Data
Energy Technology Data Exchange (ETDEWEB)
Kim, Yochan; Park, Jinkyun; Kim, Seunghwan; Choi, Sun Yeong; Jung, Wondea [Korea Atomic Research Institute, Daejeon (Korea, Republic of)
2016-10-15
As part of this effort, KAERI developed the Human Reliability data EXtraction (HuREX) framework and is collecting full-scope simulator-based human reliability data into the OPERA (Operator PErformance and Reliability Analysis) database. In this study, with the series of estimation research for HEPs or PSF effects, significant information for a quantitative HRA analysis, recovery failure probabilities (RFPs), were produced from the OPERA database. Unsafe acts can occur at any time in safety-critical systems and the operators often manage the systems by discovering their errors and eliminating or mitigating them. To model the recovery processes or recovery strategies, there were several researches that categorize the recovery behaviors. Because the recent human error trends are required to be considered during a human reliability analysis, Jang et al. can be seen as an essential effort of the data collection. However, since the empirical results regarding soft controls were produced from a controlled laboratory environment with student participants, it is necessary to analyze a wide range of operator behaviors using full-scope simulators. This paper presents the statistics related with human error recovery behaviors obtained from the full-scope simulations that in-site operators participated in. In this study, the recovery effects by shift changes or technical support centers were not considered owing to a lack of simulation data.
Directory of Open Access Journals (Sweden)
Orlov A. I.
2015-05-01
Full Text Available According to the new paradigm of applied mathematical statistics one should prefer non-parametric methods and models. However, in applied statistics we currently use a variety of parametric models. The term "parametric" means that the probabilistic-statistical model is fully described by a finite-dimensional vector of fixed dimension, and this dimension does not depend on the size of the sample. In parametric statistics the estimation problem is to estimate the unknown value (for statistician of parameter by means of the best (in some sense method. In the statistical problems of standardization and quality control we use a three-parameter family of gamma distributions. In this article, it is considered as an example of the parametric distribution family. We compare the methods for estimating the parameters. The method of moments is universal. However, the estimates obtained with the help of method of moments have optimal properties only in rare cases. Maximum likelihood estimation (MLE belongs to the class of the best asymptotically normal estimates. In most cases, analytical solutions do not exist; therefore, to find MLE it is necessary to apply numerical methods. However, the use of numerical methods creates numerous problems. Convergence of iterative algorithms requires justification. In a number of examples of the analysis of real data, the likelihood function has many local maxima, and because of that natural iterative procedures do not converge. We suggest the use of one-step estimates (OS-estimates. They have equally good asymptotic properties as the maximum likelihood estimators, under the same conditions of regularity that MLE. One-step estimates are written in the form of explicit formulas. In this article it is proved that the one-step estimates are the best asymptotically normal estimates (under natural conditions. We have found OS-estimates for the gamma distribution and given the results of calculations using data on operating time
Directory of Open Access Journals (Sweden)
Breno Carvalho
2013-10-01
Full Text Available This paper purpose is to implement a computational program to estimate the states (complex nodal voltages of a power system and showing that the largest normalized residual (LNR test fails many times. The chosen solution method was the Weighted Least Squares (WLS. Once the states are estimated a gross error analysis is made with the purpose to detect and identify the measurements that may contain gross errors (GEs, which can interfere in the estimated states, leading the process to an erroneous state estimation. If a measure is identified as having error, it is discarded of the measurement set and the whole process is remade until all measures are within an acceptable error threshold. To validate the implemented software there have been done several computer simulations in the IEEE´s systems of 6 and 14 buses, where satisfactory results were obtained. Another purpose is to show that even a widespread method as the LNR test is subjected to serious conceptual flaws, probably due to a lack of mathematical foundation attendance in the methodology. The paper highlights the need for continuous improvement of the employed techniques and a critical view, on the part of the researchers, to see those types of failures.
Biosensor Arrays for Estimating Molecular Concentration in Fluid Flows
Abolfath-Beygi, Maryam
2011-01-01
This paper constructs dynamical models and estimation algorithms for the concentration of target molecules in a fluid flow using an array of novel biosensors. Each biosensor is constructed out of protein molecules embedded in a synthetic cell membrane. The concentration evolves according to an advection-diffusion partial differential equation which is coupled with chemical reaction equations on the biosensor surface. By using averaging theory methods and the divergence theorem, an approximate model is constructed that describes the asymptotic behaviour of the concentration as a system of ordinary differential equations. The estimate of target molecules is then obtained by solving a nonlinear least squares problem. It is shown that the estimator is strongly consistent and asymptotically normal. An explicit expression is obtained for the asymptotic variance of the estimation error. As an example, the results are illustrated for a novel biosensor built out of protein molecules.
Asymptotics of bivariate generating functions with algebraic singularities
Greenwood, Torin
Flajolet and Odlyzko (1990) derived asymptotic formulae the coefficients of a class of uni- variate generating functions with algebraic singularities. Gao and Richmond (1992) and Hwang (1996, 1998) extended these results to classes of multivariate generating functions, in both cases by reducing to the univariate case. Pemantle and Wilson (2013) outlined new multivariate ana- lytic techniques and used them to analyze the coefficients of rational generating functions. After overviewing these methods, we use them to find asymptotic formulae for the coefficients of a broad class of bivariate generating functions with algebraic singularities. Beginning with the Cauchy integral formula, we explicity deform the contour of integration so that it hugs a set of critical points. The asymptotic contribution to the integral comes from analyzing the integrand near these points, leading to explicit asymptotic formulae. Next, we use this formula to analyze an example from current research. In the following chapter, we apply multivariate analytic techniques to quan- tum walks. Bressler and Pemantle (2007) found a (d + 1)-dimensional rational generating function whose coefficients described the amplitude of a particle at a position in the integer lattice after n steps. Here, the minimal critical points form a curve on the (d + 1)-dimensional unit torus. We find asymptotic formulae for the amplitude of a particle in a given position, normalized by the number of steps n, as n approaches infinity. Each critical point contributes to the asymptotics for a specific normalized position. Using Groebner bases in Maple again, we compute the explicit locations of peak amplitudes. In a scaling window of size the square root of n near the peaks, each amplitude is asymptotic to an Airy function.
Variable bandwidth and one-step local M-estimator
Institute of Scientific and Technical Information of China (English)
范剑青; 蒋建成
2000-01-01
A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of robustness of least-squares techniques. The use of variable bandwidth enhances the flexibility of the resulting local M- estimators and makes them possible to cope well with spatially inho-mogeneous curves, heteroscedastic errors and nonuniform design densities. Under appropriate regularity conditions, it is shown that the proposed estimators exist and are asymptotically normal. Based on the robust estimation equation, one-step local M-estimators are introduced to reduce computational burden. It is demonstrated that the one-step local M-estimators share the same asymptotic distributions as the fully iterative M-estimators, as long as the initial estimators are good enough. In other words, the one-step local M-estimators reduce significantly the computation cost of the fully iterative M-estim
Superradiant instabilities of asymptotically anti-de Sitter black holes
Green, Stephen R.; Hollands, Stefan; Ishibashi, Akihiro; Wald, Robert M.
2016-06-01
We study the linear stability of asymptotically anti-de Sitter black holes in general relativity in spacetime dimension d≥slant 4. Our approach is an adaptation of the general framework of Hollands and Wald, which gives a stability criterion in terms of the sign of the canonical energy, { E }. The general framework was originally formulated for static or stationary and axisymmetric black holes in the asymptotically flat case, and the stability analysis for that case applies only to axisymmetric perturbations. However, in the asymptotically anti-de Sitter case, the stability analysis requires only that the black hole have a single Killing field normal to the horizon and there are no restrictions on the perturbations (apart from smoothness and appropriate behavior at infinity). For an asymptotically anti-de Sitter black hole, we define an ergoregion to be a region where the horizon Killing field is spacelike; such a region, if present, would normally occur near infinity. We show that for black holes with ergoregions, initial data can be constructed such that { E }\\lt 0, so all such black holes are unstable. To obtain such initial data, we first construct an approximate solution to the constraint equations using the WKB method, and then we use the Corvino-Schoen technique to obtain an exact solution. We also discuss the case of charged asymptotically anti-de Sitter black holes with generalized ergoregions.
Asymptotic aspects of Cayley graphs
Dejter, Italo J
2011-01-01
Arising from complete Cayley graphs $\\Gamma_n$ of odd cyclic groups $\\Z_n$, an asymptotic approach is presented on connected labeled graphs whose vertices are labeled via equally-multicolored copies of $K_4$ in $\\Gamma_n$ with adjacency of any two such vertices whenever they are represented by copies of $K_4$ in $\\Gamma_n$ sharing two equally-multicolored triangles. In fact, these connected labeled graphs are shown to form a family of graphs of largest degree 6 and diameter asymptotically of order $|V|^{1/3}$, properties shared by the initial member of a collection of families of Cayley graphs of degree $2m\\geq 6$ with diameter asymptotically of order $|V|^{1/m}$, where $3\\leq m\\in\\Z$.
Asymptotic analysis and boundary layers
Cousteix, Jean
2007-01-01
This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general comprehensive presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows. The advantages of SCEM are discussed in comparison with the standard Method of Matched Asymptotic Expansions. In particular, for the first time, the theory of Interactive Boundary Layer is fully justified. With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is self-contained. It is written on a mathematical level accessible to graduate and post-graduate students of engineering and physics with a good knowledge in fluid mechanics. Researchers and practitioners will estee...
Asymptotic vacua with higher derivatives
Directory of Open Access Journals (Sweden)
Spiros Cotsakis
2016-04-01
Full Text Available We study limits of vacuum, isotropic universes in the full, effective, four-dimensional theory with higher derivatives. We show that all flat vacua as well as general curved ones are globally attracted by the standard, square root scaling solution at early times. Open vacua asymptote to horizon-free, Milne states in both directions while closed universes exhibit more complex logarithmic singularities, starting from initial data sets of a possibly smaller dimension. We also discuss the relation of our results to the asymptotic stability of the passage through the singularity in ekpyrotic and cyclic cosmologies.
Asymptotic vacua with higher derivatives
Energy Technology Data Exchange (ETDEWEB)
Cotsakis, Spiros, E-mail: skot@aegean.gr [Department of Mathematics, American University of the Middle East, P.O. Box 220 Dasman, 15453 (Kuwait); Kadry, Seifedine, E-mail: Seifedine.Kadry@aum.edu.kw [Department of Mathematics, American University of the Middle East, P.O. Box 220 Dasman, 15453 (Kuwait); Kolionis, Georgios, E-mail: gkolionis@aegean.gr [Research group of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos (Greece); Tsokaros, Antonios, E-mail: atsok@aegean.gr [Research group of Geometry, Dynamical Systems and Cosmology, University of the Aegean, Karlovassi 83200, Samos (Greece)
2016-04-10
We study limits of vacuum, isotropic universes in the full, effective, four-dimensional theory with higher derivatives. We show that all flat vacua as well as general curved ones are globally attracted by the standard, square root scaling solution at early times. Open vacua asymptote to horizon-free, Milne states in both directions while closed universes exhibit more complex logarithmic singularities, starting from initial data sets of a possibly smaller dimension. We also discuss the relation of our results to the asymptotic stability of the passage through the singularity in ekpyrotic and cyclic cosmologies.
Expansions and Asymptotics for Statistics
Small, Christopher G
2010-01-01
Providing a broad toolkit of analytical methods, this book shows how asymptotics, when coupled with numerical methods, becomes a powerful way to acquire a deeper understanding of the techniques used in probability and statistics. It describes core ideas in statistical asymptotics; covers Laplace approximation, the saddle-point method, and summation of series; and, includes vignettes of various people from statistics and mathematics whose ideas have been instrumental in the development of the subject. The author also supplements some topics with relevant Maplea commands and provides a list of c
Asymptotic Rayleigh instantaneous unit hydrograph
Troutman, B.M.; Karlinger, M.R.
1988-01-01
The instantaneous unit hydrograph for a channel network under general linear routing and conditioned on the network magnitude, N, tends asymptotically, as N grows large, to a Rayleigh probability density function. This behavior is identical to that of the width function of the network, and is proven under the assumption that the network link configuration is topologically random and the link hydraulic and geometric properties are independent and identically distributed random variables. The asymptotic distribution depends only on a scale factor, {Mathematical expression}, where ?? is a mean link wave travel time. ?? 1988 Springer-Verlag.
Asymptotics for dissipative nonlinear equations
Hayashi, Nakao; Kaikina, Elena I; Shishmarev, Ilya A
2006-01-01
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Higher dimensional nonclassical eigenvalue asymptotics
Camus, Brice; Rautenberg, Nils
2015-02-01
In this article, we extend Simon's construction and results [B. Simon, J. Funct. Anal. 53(1), 84-98 (1983)] for leading order eigenvalue asymptotics to n-dimensional Schrödinger operators with non-confining potentials given by Hn α = - Δ + ∏ i = 1 n |x i| α i on ℝn (n > 2), α ≔ ( α 1 , … , α n ) ∈ ( R+ ∗ ) n . We apply the results to also derive the leading order spectral asymptotics in the case of the Dirichlet Laplacian -ΔD on domains Ωn α = { x ∈ R n : ∏ j = 1 n }x j| /α j α n < 1 } .
Asymptotic geometric analysis, part I
Artstein-Avidan, Shiri
2015-01-01
The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomen
An estimating function approach to inference for inhomogeneous Neyman-Scott processes
DEFF Research Database (Denmark)
Waagepetersen, Rasmus
2007-01-01
This article is concerned with inference for a certain class of inhomogeneous Neyman-Scott point processes depending on spatial covariates. Regression parameter estimates obtained from a simple estimating function are shown to be asymptotically normal when the "mother" intensity for the Neyman-Sc...
Efficient Estimation for Diffusions Sampled at High Frequency Over a Fixed Time Interval
DEFF Research Database (Denmark)
Jakobsen, Nina Munkholt; Sørensen, Michael
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find easily verified conditions on approximate martingale...... estimating functions under which estimators are consistent, rate optimal, and efficient under high frequency (in-fill) asymptotics. The asymptotic distributions of the estimators are shown to be normal variance-mixtures, where the mixing distribution generally depends on the full sample path of the diffusion...
DEFF Research Database (Denmark)
Christensen, Bent Jesper; Varneskov, Rasmus T.
band least squares (MBLS) estimator uses sample dependent trimming of frequencies in the vicinity of the origin to account for such contamination. Consistency and asymptotic normality of the MBLS estimator are established, a feasible inference procedure is proposed, and rigorous tools for assessing...... the cointegration strength and testing MBLS against the existing narrow band least squares estimator are developed. Finally, the asymptotic framework for the MBLS estimator is used to provide new perspectives on volatility factors in an empirical application to long-span realized variance series for S&P 500...
TAIL INDEX ESTIMATION FOR A FILTERED DEPENDENT TIME SERIES
National Research Council Canada - National Science Library
Jonathan B. Hill
2015-01-01
We prove Hill's (1975) tail index estimator is asymptotically normal when the employed data are generated by a stationary parametric time series (xt(θ0) : t ∈ ℤ} and θ0 is an unknown k × 1 vector. We assume xt(θ0...
Energy Technology Data Exchange (ETDEWEB)
Aid, R.
1998-01-07
This work comes from an industrial problem of validating numerical solutions of ordinary differential equations modeling power systems. This problem is solved using asymptotic estimators of the global error. Four techniques are studied: Richardson estimator (RS), Zadunaisky's techniques (ZD), integration of the variational equation (EV), and Solving for the correction (SC). We give some precisions on the relative order of SC w.r.t. the order of the numerical method. A new variant of ZD is proposed that uses the Modified Equation. In the case of variable step-size, it is shown that under suitable restriction, on the hypothesis of the step-size selection, ZD and SC are still valid. Moreover, some Runge-Kutta methods are shown to need less hypothesis on the step-sizes to exhibit a valid order of convergence for ZD and SC. Numerical tests conclude this analysis. Industrial cases are given. Finally, an algorithm to avoid the a priori specification of the integration path for complex time differential equations is proposed. (author)
Asymptotic distributions for a class of generalized $L$-statistics
Borovskikh, Yuri V; 10.3150/09-BEJ240
2010-01-01
We adapt the techniques in Stigler [Ann. Statist. 1 (1973) 472--477] to obtain a new, general asymptotic result for trimmed $U$-statistics via the generalized $L$-statistic representation introduced by Serfling [Ann. Statist. 12 (1984) 76--86]. Unlike existing results, we do not require continuity of an associated distribution at the truncation points. Our results are quite general and are expressed in terms of the quantile function associated with the distribution of the $U$-statistic summands. This approach leads to improved conditions for the asymptotic normality of these trimmed $U$-statistics.
SEMI PARAMETRIC ESTIMATION OF RISK-RETURN RELATIONSHIPS
Juan Carlos Escanciano; Juan Carlos Pardo-Fernández; Ingrid Van Keilegom
2013-01-01
This article proposes semi-parametric least squares estimation of parametric risk-return relationships, i.e. parametric restrictions between the conditional mean and the conditional variance of excess returns given a set of unobservable parametric factors. A distinctive feature of our estimator is that it does not require a parametric model for the conditional mean and variance. We establish consistency and asymptotic normality of the estimates. The theory is non-standard due to the presence ...
Ruin problems and tail asymptotics
DEFF Research Database (Denmark)
Rønn-Nielsen, Anders
The thesis Ruin Problems and Tail Asymptotics provides results on ruin problems for several classes of Markov processes. For a class of diffusion processes with jumps an explicit expression for the joint Laplace transform of the first passage time and the corresponding undershoot is derived...
Inaccurate usage of asymptotic formulas
Maj, R; Maj, Radoslaw; Mrowczynski, Stanislaw
2004-01-01
The asymptotic form of the plane-wave decomposition into spherical waves, which is often used, in particular, to express the scattering amplitude through the phase shifts, is incorrect. We precisely explain why it is incorrect and show how to circumvent mathematical inconsistency.
Thermodynamics of asymptotically safe theories
DEFF Research Database (Denmark)
Rischke, Dirk H.; Sannino, Francesco
2015-01-01
We investigate the thermodynamic properties of a novel class of gauge-Yukawa theories that have recently been shown to be completely asymptotically safe, because their short-distance behaviour is determined by the presence of an interacting fixed point. Not only do all the coupling constants freeze...
Asymptotic solution of nonlinear moment equations for constant-rate aerosol reactors
Directory of Open Access Journals (Sweden)
B. D. Shaw
1998-01-01
Full Text Available Nonlinear evolution equations based upon moments of the aerosol size distribution function are solved asymptotically for constant-rate aerosol reactors (i.e., where condensible monomer is added at a constant rate operating in the free-molecular limit. The governing equations are nondimensionalized and a large parameter that controls nucleation behavior is identified. Asymptotic analyses are developed in terms of this parameter. Comparison of the asymptotic results with direct numerical integration of the governing equations is favorable. The asymptotic results provide a simplified analytical approach to estimating average particle sizes, particle number densities, and peak supersaturation values for constant-rate aerosol reactors.
Muro, Javier; Heinmann, Sascha; Strauch, Adrian; Menz, Gunter
2016-08-01
Land Surface Temperature (LST) has the potential to act as a continuous indicator of the ecological status of wetlands. Accurate emissivity values are required in order to calculate precise LST. We test two emissivity retrieval methods and their influence on LST calculated from a Landsat 7 image of a highly dynamic wetland in Southern Spain. LST calculated using NDVI (Normalized Difference Vegetation Index) threshold estimations and the ASTER emissivity product are compared. The results show differences of around 0-1 K for most land covers, and up to 3 K for areas of bare soil when Landsat and ASTER images have the same acquisition date. Tests using Landsat and ASTER images from different seasons do not show greater differences between both LSTs. This has important implications for automated LST retrieval methods, such as the one planed by the USGS using Landsat and ASTER emissivity products.
Asymptotic Behavior of the Finite Difference and the Finite Element Methods for Parabolic Equations
Institute of Scientific and Technical Information of China (English)
LIU Yang; FENG Hui
2005-01-01
The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are asymptotically convergent. Both methods are considered in continuous time.
Exact tail asymptotics of the supremum attained by a Lévy process
Asghari, N.M.; Dębicki, K.; Mandjes, M.
2015-01-01
In this short communication we analyze the tail asymptotics corresponding to the maximum value attained by a Lévy process with negative drift. The note has two contributions: a short and elementary proof of these asymptotics, and an importance sampling algorithm to estimate the rare-event probabilit
Small Bandwidth Asymptotics for Density-Weighted Average Derivatives
DEFF Research Database (Denmark)
Cattaneo, Matias D.; Crump, Richard K.; Jansson, Michael
This paper proposes (apparently) novel standard error formulas for the density-weighted average derivative estimator of Powell, Stock, and Stoker (1989). Asymptotic validity of the standard errors developed in this paper does not require the use of higher-order kernels and the standard errors...
On transfinite extension of asymptotic dimension
Radul, Taras
2006-01-01
We prove that a transfinite extension of asymptotic dimension asind is trivial. We introduce a transfinite extension of asymptotic dimension asdim and give an example of metric proper space which has transfinite infinite dimension.
Size Matters: Individual Variation in Ectotherm Growth and Asymptotic Size
King, Richard B.
2016-01-01
Body size, and, by extension, growth has impacts on physiology, survival, attainment of sexual maturity, fecundity, generation time, and population dynamics, especially in ectotherm animals that often exhibit extensive growth following attainment of sexual maturity. Frequently, growth is analyzed at the population level, providing useful population mean growth parameters but ignoring individual variation that is also of ecological and evolutionary significance. Our long-term study of Lake Erie Watersnakes, Nerodia sipedon insularum, provides data sufficient for a detailed analysis of population and individual growth. We describe population mean growth separately for males and females based on size of known age individuals (847 captures of 769 males, 748 captures of 684 females) and annual growth increments of individuals of unknown age (1,152 males, 730 females). We characterize individual variation in asymptotic size based on repeated measurements of 69 males and 71 females that were each captured in five to nine different years. The most striking result of our analyses is that asymptotic size varies dramatically among individuals, ranging from 631–820 mm snout-vent length in males and from 835–1125 mm in females. Because female fecundity increases with increasing body size, we explore the impact of individual variation in asymptotic size on lifetime reproductive success using a range of realistic estimates of annual survival. When all females commence reproduction at the same age, lifetime reproductive success is greatest for females with greater asymptotic size regardless of annual survival. But when reproduction is delayed in females with greater asymptotic size, lifetime reproductive success is greatest for females with lower asymptotic size when annual survival is low. Possible causes of individual variation in asymptotic size, including individual- and cohort-specific variation in size at birth and early growth, warrant further investigation. PMID
Precise Asymptotics for Random Matrices and Random Growth Models
Institute of Scientific and Technical Information of China (English)
Zhong Gen SU
2008-01-01
The author considers the largest eigenvalues of random matrices from Gaussian unitary ensemble and Laguerre unitary ensemble, and the rightmost charge in certain random growth models.We obtain some precise asymptotics results, which are in a sense similar to the precise asymptotics for sums of independent random variables in the context of the law of large numbers and complete convergence. Our proofs depend heavily upon the upper and lower tail estimates for random matrices and random growth models. The Tracy-Widom distribution plays a central role as well.
Penalized maximum likelihood estimation and variable selection in geostatistics
Chu, Tingjin; Wang, Haonan; 10.1214/11-AOS919
2012-01-01
We consider the problem of selecting covariates in spatial linear models with Gaussian process errors. Penalized maximum likelihood estimation (PMLE) that enables simultaneous variable selection and parameter estimation is developed and, for ease of computation, PMLE is approximated by one-step sparse estimation (OSE). To further improve computational efficiency, particularly with large sample sizes, we propose penalized maximum covariance-tapered likelihood estimation (PMLE$_{\\mathrm{T}}$) and its one-step sparse estimation (OSE$_{\\mathrm{T}}$). General forms of penalty functions with an emphasis on smoothly clipped absolute deviation are used for penalized maximum likelihood. Theoretical properties of PMLE and OSE, as well as their approximations PMLE$_{\\mathrm{T}}$ and OSE$_{\\mathrm{T}}$ using covariance tapering, are derived, including consistency, sparsity, asymptotic normality and the oracle properties. For covariance tapering, a by-product of our theoretical results is consistency and asymptotic normal...
On an asymptotic distribution of dependent random variables on a 3-dimensional lattice.
Harvey, Danielle J; Weng, Qian; Beckett, Laurel A
2010-06-15
We define conditions under which sums of dependent spatial data will be approximately normally distributed. A theorem on the asymptotic distribution of a sum of dependent random variables defined on a 3-dimensional lattice is presented. Examples are also presented.
Liu, Fu-Dong; Pan, Zi-Qiang; Liu, Sen-Lin; Chen, Ling; Chen, Lu; Wang, Chun-Hong
2017-04-28
Due to the improvement of production technology and the adjustment of energy structure, as well as the town-ownership and private-ownership coal mines (TPCM) were closed or merged by national policy, the number of underground miner has changed comparing with 2004 in China, so collective dose and normalization collective dose in different type of coal mine should be changed at the same time. In this paper, according to radiation exposure by different ventilation condition and the annual output, the coal mines in China are divided into three types, which are named as national key coal mines (NKCM), station-owned local coal mines (SLCM) and TPCM. The number of underground coal miner, collective dose and normalization collective dose are estimated at present base on surveying annual output and production efficiency of raw coal in 2005-2014. The typical total value of the underground coal miners recommended in China is 5.1 million in 2005-2009, and in which there are respectively included 1 million, 0.9 million and 3.2 million for NKCM, SLCM and TPCM. There are total of 4.7 million underground coal miner in 2010-2014, and the respectively number for NKCM, SLCM and TPCM are 1.4 million, 1.2 million and 2.1 million. The collective dose in 2005-2009 is 11 335 man·Sv·y-1, and in which there are respectively included 280, 495 and 10 560 man·Sv·y-1 for NKCM, SLCM and TPCM. As far as 2010-2014, there are total of 7982 man·Sv·y-1, and 392, 660 and 6930 man·Sv·y-1 for each type of coal mines. Therefore, the main contributor of collective dose is from TPCM. The normalization collective dose in 2005-2009 is 0.0025, 0.015 and 0.117 man·Sv per 10 kt for NKCM, SLCM and TPCM, respectively. As far as 2010-2014, there are 0.0018, 0.010 and 0.107 man·Sv per 10 kt for each type of coal mines. The trend of normalization collective dose is decreased year by year. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please
An Estimator of Heavy Tail Index through the Generalized Jackknife Methodology
Directory of Open Access Journals (Sweden)
Weiqi Liu
2014-01-01
Full Text Available In practice, sometimes the data can be divided into several blocks but only a few of the largest observations within each block are available to estimate the heavy tail index. To address this problem, we propose a new class of estimators through the Generalized Jackknife methodology based on Qi’s estimator (2010. These estimators are proved to be asymptotically normal under suitable conditions. Compared to Hill’s estimator and Qi’s estimator, our new estimator has better asymptotic efficiency in terms of the minimum mean squared error, for a wide range of the second order shape parameters. For the finite samples, our new estimator still compares favorably to Hill’s estimator and Qi’s estimator, providing stable sample paths as a function of the number of dividing the sample into blocks, smaller estimation bias, and MSE.
Two-stage local M-estimation of additive models
Institute of Scientific and Technical Information of China (English)
JIANG JianCheng; LI JianTao
2008-01-01
This paper studies local M-estimation of the nonparametric components of additive models. A two-stage local M-estimation procedure is proposed for estimating the additive components and their derivatives. Under very mild conditions, the proposed estimators of each additive component and its derivative are jointly asymptotically normal and share the same asymptotic distributions as they would be if the other components were known. The established asymptotic results also hold for two particular local M-estimations: the local least squares and least absolute deviation estimations. However,for general two-stage local M-estimation with continuous and nonlinear ψ-functions, its implementation is time-consuming. To reduce the computational burden, one-step approximations to the two-stage local M-estimators are developed. The one-step estimators are shown to achieve the same efficiency as the fully iterative two-stage local M-estimators, which makes the two-stage local M-estimation more feasible in practice. The proposed estimators inherit the advantages and at the same time overcome the disadvantages of the local least-squares based smoothers. In addition, the practical implementation of the proposed estimation is considered in details. Simulations demonstrate the merits of the two-stage local M-estimation, and a real example illustrates the performance of the methodology.
Two-stage local M-estimation of additive models
Institute of Scientific and Technical Information of China (English)
2008-01-01
This paper studies local M-estimation of the nonparametric components of additive models.A two-stage local M-estimation procedure is proposed for estimating the additive components and their derivatives.Under very mild conditions,the proposed estimators of each additive component and its derivative are jointly asymptotically normal and share the same asymptotic distributions as they would be if the other components were known.The established asymptotic results also hold for two particular local M-estimations:the local least squares and least absolute deviation estimations.However,for general two-stage local M-estimation with continuous and nonlinear ψ-functions,its implementation is time-consuming.To reduce the computational burden,one-step approximations to the two-stage local M-estimators are developed.The one-step estimators are shown to achieve the same effciency as the fully iterative two-stage local M-estimators,which makes the two-stage local M-estimation more feasible in practice.The proposed estimators inherit the advantages and at the same time overcome the disadvantages of the local least-squares based smoothers.In addition,the practical implementation of the proposed estimation is considered in details.Simulations demonstrate the merits of the two-stage local M-estimation,and a real example illustrates the performance of the methodology.
Nonabelian Higgs models: paving the way for asymptotic freedom
Gies, Holger
2016-01-01
Asymptotically free renormalization group trajectories can be constructed in nonabelian Higgs models with the aid of generalized boundary conditions imposed on the renormalized action. We detail this construction within the languages of simple low-order perturbation theory, effective field theory, as well as modern functional renormalization group equations. We construct a family of explicit scaling solutions using a controlled weak-coupling expansion in the ultraviolet, and obtain a standard Wilsonian RG relevance classification of perturbations about scaling solutions. We obtain global information about the quasi-fixed function for the scalar potential by means of analytic asymptotic expansions and numerical shooting methods. Further analytical evidence for such asymptotically free theories is provided in the large-N limit. We estimate the long-range properties of these theories, and identify initial/boundary conditions giving rise to a conventional Higgs phase.
Empirical likelihood estimation of discretely sampled processes of OU type
Institute of Scientific and Technical Information of China (English)
2009-01-01
This paper presents an empirical likelihood estimation procedure for parameters of the discretely sampled process of Ornstein-Uhlenbeck type. The proposed procedure is based on the condi- tional characteristic function, and the maximum empirical likelihood estimator is proved to be consistent and asymptotically normal. Moreover, this estimator is shown to be asymptotically efficient under some mild conditions. When the background driving Lévy process is of type A or B, we show that the intensity parameter can be exactly recovered, and we study the maximum empirical likelihood estimator with the plug-in estimated intensity parameter. Testing procedures based on the empirical likelihood ratio statistic are developed for parameters and for estimating equations, respectively. Finally, Monte Carlo simulations are conducted to demonstrate the performance of proposed estimators.
Remarks on asymptotically safe inflation
Tye, S.-H. Henry; Xu, Jiajun
2010-12-01
We comment on Weinberg’s interesting analysis of asymptotically safe inflation [S. Weinberg, Phys. Rev. DPRVDAQ1550-7998 81, 083535 (2010).10.1103/PhysRevD.81.083535]. We find that even if the gravity theory exhibits an ultraviolet fixed point, the energy scale during inflation is way too low to drive the theory close to the fixed point value. We choose the specific renormalization group flow away from the fixed point towards the infrared region that reproduces the Newton’s constant and today’s cosmological constant. We follow this renormalization group flow path to scales below the Planck scale to study the stability of the inflationary scenario. Again, we find that some fine-tuning is necessary to get enough e folds of inflation in the asymptotically safe inflationary scenario.
Asymptotic safety goes on shell
Benedetti, Dario
2012-01-01
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector and a new cut-off scheme. We find a nontrivial fixed point, with a value of the cosmological constant that is independent of the gauge-fixing parameters.
Asymptotic Excisions of Metric Spaces and Ideals of Asymptotic Coarse Roe Algebras
Institute of Scientific and Technical Information of China (English)
LI Jin-xiu; WANG Qin
2006-01-01
We introduce in this note the notions of asymptotic excision of proper metric spaces and asymptotic equivalence relation for subspaces of metric spaces, which are relevant in characterizing spatial ideals of the asymptotic coarse Roe algebras. We show that the lattice of the asymptotic equivalence classes of the subspaces of a proper metric space is isomorphic to the lattice of the spatial ideals of the asymptotic Roe algebra. For asymptotic excisions of the metric space, we also establish a Mayer-Vietoris sequence in K-theory of the asymptotic coarse Roe algebras.
Motion Parallax is Asymptotic to Binocular Disparity
Stroyan, Keith
2010-01-01
Researchers especially beginning with (Rogers & Graham, 1982) have noticed important psychophysical and experimental similarities between the neurologically different motion parallax and stereopsis cues. Their quantitative analysis relied primarily on the "disparity equivalence" approximation. In this article we show that retinal motion from lateral translation satisfies a strong ("asymptotic") approximation to binocular disparity. This precise mathematical similarity is also practical in the sense that it applies at normal viewing distances. The approximation is an extension to peripheral vision of (Cormac & Fox's 1985) well-known non-trig central vision approximation for binocular disparity. We hope our simple algebraic formula will be useful in analyzing experiments outside central vision where less precise approximations have led to a number of quantitative errors in the vision literature.
Hydrodynamics, resurgence and trans-asymptotics
Basar, Gokce
2015-01-01
The second-order hydrodynamical description of a homogeneous conformal plasma that undergoes a boost- invariant expansion is given by a single nonlinear ordinary differential equation, whose resurgent asymptotic properties we study, developing further the recent work of Heller and Spalinski [Phys. Rev. Lett. 115, 072501 (2015)]. Resurgence clearly identifies the non-hydrodynamic modes that are exponentially suppressed at late times, analogous to the quasi-normal-modes in gravitational language, organizing these modes in terms of a trans-series expansion. These modes are analogs of instantons in semi-classical expansions, where the damping rate plays the role of the instanton action. We show that this system displays the generic features of resurgence, with explicit quantitative relations between the fluctuations about different orders of these non-hydrodynamic modes. The imaginary part of the trans-series parameter is identified with the Stokes constant, and the real part with the freedom associated with init...
Asymptotic results for bifurcating random coefficient autoregressive processes
Blandin, Vassili
2012-01-01
The purpose of this paper is to study the asymptotic behavior of the weighted least square estimators of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on the immigration and the inheritance, we establish the almost sure convergence of our estimators, as well as a quadratic strong law and central limit theorems. Our study mostly relies on limit theorems for vector-valued martingales.
Superradiant instabilities of asymptotically anti-de Sitter black holes
Green, Stephen R; Ishibashi, Akihiro; Wald, Robert M
2015-01-01
We study the linear stability of asymptotically anti-de Sitter black holes in general relativity in spacetime dimension $d\\ge4$. Our approach is an adaptation of the general framework of Hollands and Wald, which gives a stability criterion in terms of the sign of the canonical energy, $\\mathcal{E}$. The general framework was originally formulated for static or stationary and axisymmetric black holes in the asymptotically flat case, and the stability analysis for that case applies only to axisymmetric perturbations. However, in the asymptotically anti-de Sitter case, the stability analysis requires only that the black hole have a single Killing field normal to the horizon and there are no restrictions on the perturbations (apart from smoothness and appropriate behavior at infinity). For an asymptotically anti-de Sitter black hole, we define an ergoregion to be a region where the horizon Killing field is spacelike; such a region, if present, would normally occur near infinity. We show that for black holes with ...
Supersymmetric asymptotic safety is not guaranteed
Intriligator, Kenneth
2015-01-01
It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those of an asymptotically free (perhaps magnetic dual) extension.
Asymptotic integration of differential and difference equations
Bodine, Sigrun
2015-01-01
This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers i...
Generalized multiplicative error models: Asymptotic inference and empirical analysis
Li, Qian
This dissertation consists of two parts. The first part focuses on extended Multiplicative Error Models (MEM) that include two extreme cases for nonnegative series. These extreme cases are common phenomena in high-frequency financial time series. The Location MEM(p,q) model incorporates a location parameter so that the series are required to have positive lower bounds. The estimator for the location parameter turns out to be the minimum of all the observations and is shown to be consistent. The second case captures the nontrivial fraction of zero outcomes feature in a series and combines a so-called Zero-Augmented general F distribution with linear MEM(p,q). Under certain strict stationary and moment conditions, we establish a consistency and asymptotic normality of the semiparametric estimation for these two new models. The second part of this dissertation examines the differences and similarities between trades in the home market and trades in the foreign market of cross-listed stocks. We exploit the multiplicative framework to model trading duration, volume per trade and price volatility for Canadian shares that are cross-listed in the New York Stock Exchange (NYSE) and the Toronto Stock Exchange (TSX). We explore the clustering effect, interaction between trading variables, and the time needed for price equilibrium after a perturbation for each market. The clustering effect is studied through the use of univariate MEM(1,1) on each variable, while the interactions among duration, volume and price volatility are captured by a multivariate system of MEM(p,q). After estimating these models by a standard QMLE procedure, we exploit the Impulse Response function to compute the calendar time for a perturbation in these variables to be absorbed into price variance, and use common statistical tests to identify the difference between the two markets in each aspect. These differences are of considerable interest to traders, stock exchanges and policy makers.
Optimal adaptive normalized matched filter for large antenna arrays
Kammoun, Abla
2016-09-13
This paper focuses on the problem of detecting a target in the presence of a compound Gaussian clutter with unknown statistics. To this end, we focus on the design of the adaptive normalized matched filter (ANMF) detector which uses the regularized Tyler estimator (RTE) built from N-dimensional observations x, · · ·, x in order to estimate the clutter covariance matrix. The choice for the RTE is motivated by its possessing two major attributes: first its resilience to the presence of outliers, and second its regularization parameter that makes it more suitable to handle the scarcity in observations. In order to facilitate the design of the ANMF detector, we consider the regime in which n and N are both large. This allows us to derive closed-form expressions for the asymptotic false alarm and detection probabilities. Based on these expressions, we propose an asymptotically optimal setting for the regularization parameter of the RTE that maximizes the asymptotic detection probability while keeping the asymptotic false alarm probability below a certain threshold. Numerical results are provided in order to illustrate the gain of the proposed detector over a recently proposed setting of the regularization parameter.
Energy Technology Data Exchange (ETDEWEB)
Kim, Jun Hwee; Kim, Myung Joon; Lim, Sok Hwan; Lee, Mi Jung [Dept. of Radiology and Research Institute of Radiological Science, Severance Children' s Hospital, Yonsei University College of Medicine, Seoul (Korea, Republic of); Kim, Ji Eun [Biostatistics Collaboration Unit, Yonsei University College of Medicine, Seoul (Korea, Republic of)
2013-08-15
To evaluate the relationship between anthropometric measurements and renal length and volume measured with ultrasound in Korean children who have morphologically normal kidneys, and to create simple equations to estimate the renal sizes using the anthropometric measurements. We examined 794 Korean children under 18 years of age including a total of 394 boys and 400 girls without renal problems. The maximum renal length (L) (cm), orthogonal anterior-posterior diameter (D) (cm) and width (W) (cm) of each kidney were measured on ultrasound. Kidney volume was calculated as 0.523 x L x D x W (cm{sup 3}). Anthropometric indices including height (cm), weight (kg) and body mass index (m{sup 2}/kg) were collected through a medical record review. We used linear regression analysis to create simple equations to estimate the renal length and the volume with those anthropometric indices that were mostly correlated with the US-measured renal sizes. Renal length showed the strongest significant correlation with patient height (R2, 0.874 and 0.875 for the right and left kidneys, respectively, p < 0.001). Renal volume showed the strongest significant correlation with patient weight (R2, 0.842 and 0.854 for the right and left kidneys, respectively, p < 0.001). The following equations were developed to describe these relationships with an estimated 95% range of renal length and volume (R2, 0.826-0.884, p < 0.001): renal length = 2.383 + 0.045 x Height (± 1.135) and = 2.374 + 0.047 x Height (± 1.173) for the right and left kidneys, respectively; and renal volume 7.941 + 1.246 x Weight (± 15.920) and = 7.303 + 1.532 x Weight (± 18.704) for the right and left kidneys, respectively. Scatter plots between height and renal length and between weight and renal volume have been established from Korean children and simple equations between them have been developed for use in clinical practice.
Institute of Scientific and Technical Information of China (English)
RAO Calyampudi R; WU YueHua
2009-01-01
In this paper, the constrained M-estimation of the regression coefficients and scatter parameters in a general multivariate linear regression model is considered. Since the constrained Mestimation is not easy to compute, an up-dating recursion procedure is proposed to simplify the computation of the estimators when a new observation is obtained. We show that, under mild conditions,the recursion estimates are strongly consistent. In addition, the asymptotic normality of the recursive constrained M-estimators of regression coefficients is established. A Monte Carlo simulation study of the recursion estimates is also provided. Besides, robustness and asymptotic behavior of constrained M-estimators are briefly discussed.
Asymptotic properties of restricted naming games
Bhattacherjee, Biplab; Datta, Amitava; Manna, S. S.
2017-07-01
Asymptotic properties of the symmetric and asymmetric naming games have been studied under some restrictions in a community of agents. In one version, the vocabulary sizes of the agents are restricted to finite capacities. In this case, compared to the original naming games, the dynamics takes much longer time for achieving the consensus. In the second version, the symmetric game starts with a limited number of distinct names distributed among the agents. Three different quantities are measured for a quantitative comparison, namely, the maximum value of the total number of names in the community, the time at which the community attains the maximal number of names, and the global convergence time. Using an extensive numerical study, the entire set of three power law exponents characterizing these quantities are estimated for both the versions which are observed to be distinctly different from their counter parts of the original naming games.
Asymptotic behavior of solutions of the damped Boussinesq equation in two space dimensions
Directory of Open Access Journals (Sweden)
Vladimir V. Varlamov
1999-01-01
classical solution is proved and the solution is constructed in the form of a series. The major term of its long-time asymptotics is calculated explicitly and a uniform in space estimate of the residual term is given.
NONPARAMETRIC ESTIMATION OF CHARACTERISTICS OF PROBABILITY DISTRIBUTIONS
Directory of Open Access Journals (Sweden)
Orlov A. I.
2015-10-01
Full Text Available The article is devoted to the nonparametric point and interval estimation of the characteristics of the probabilistic distribution (the expectation, median, variance, standard deviation, variation coefficient of the sample results. Sample values are regarded as the implementation of independent and identically distributed random variables with an arbitrary distribution function having the desired number of moments. Nonparametric analysis procedures are compared with the parametric procedures, based on the assumption that the sample values have a normal distribution. Point estimators are constructed in the obvious way - using sample analogs of the theoretical characteristics. Interval estimators are based on asymptotic normality of sample moments and functions from them. Nonparametric asymptotic confidence intervals are obtained through the use of special output technology of the asymptotic relations of Applied Statistics. In the first step this technology uses the multidimensional central limit theorem, applied to the sums of vectors whose coordinates are the degrees of initial random variables. The second step is the conversion limit multivariate normal vector to obtain the interest of researcher vector. At the same considerations we have used linearization and discarded infinitesimal quantities. The third step - a rigorous justification of the results on the asymptotic standard for mathematical and statistical reasoning level. It is usually necessary to use the necessary and sufficient conditions for the inheritance of convergence. This article contains 10 numerical examples. Initial data - information about an operating time of 50 cutting tools to the limit state. Using the methods developed on the assumption of normal distribution, it can lead to noticeably distorted conclusions in a situation where the normality hypothesis failed. Practical recommendations are: for the analysis of real data we should use nonparametric confidence limits
Institute of Scientific and Technical Information of China (English)
Jing Wen LUAN; Fu Liu ZHU
2005-01-01
In this paper, we make the asymptotic estimates of the heat kernel for the quaternionic Heisenberg group in various cases. We also use these results to deduce the asymptotic estimates of certain harmonic functions on the quaternionic Heisenberg group. Moreover a Martin compactification of the quaternionic Heisenberg group is constructed, and we prove that the Martin boundary of this group is homeomorphic to the unit ball in the quaternionic field.
Michelotti, Erika A; Whicker, Jeffrey J; Eisele, William F; Breshears, David D; Kirchner, Thomas B
2013-06-01
Dose assessments typically consider environmental systems as static through time, but environmental disturbances such as drought and fire are normal, albeit infrequent, events that can impact dose-influential attributes of many environmental systems. These phenomena occur over time frames of decades or longer, and are likely to be exacerbated under projected warmer, drier climate. As with other types of dose assessment, the impacts of environmental disturbances are often overlooked when evaluating dose from aeolian transport of radionuclides and other contaminants. Especially lacking are predictions that account for potential changing vegetation cover effects on radionuclide transport over the long time frames required by regulations. A recently developed dynamic wind-transport model that included vegetation succession and environmental disturbance provides more realistic long-term predictability. This study utilized the model to estimate emission rates for aeolian transport, and compare atmospheric dispersion and deposition rates of airborne plutonium-contaminated soil into neighboring areas with and without environmental disturbances. Specifically, the objective of this study was to utilize the model results as input for a widely used dose assessment model (CAP-88). Our case study focused on low levels of residual plutonium found in soils from past operations at Los Alamos National Laboratory (LANL), in Los Alamos, NM, located in the semiarid southwestern USA. Calculations were conducted for different disturbance scenarios based on conditions associated with current climate, and a potential future drier and warmer climate. Known soil and sediment concentrations of plutonium were used to model dispersal and deposition of windblown residual plutonium, as a function of distance and direction. Environmental disturbances that affected vegetation cover included ground fire, crown fire, and drought, with reoccurrence rates for current climate based on site historical
Asymptotics for Associated Random Variables
Oliveira, Paulo Eduardo
2012-01-01
The book concerns the notion of association in probability and statistics. Association and some other positive dependence notions were introduced in 1966 and 1967 but received little attention from the probabilistic and statistics community. The interest in these dependence notions increased in the last 15 to 20 years, and many asymptotic results were proved and improved. Despite this increased interest, characterizations and results remained essentially scattered in the literature published in different journals. The goal of this book is to bring together the bulk of these results, presenting
Asymptotics of robust utility maximization
Knispel, Thomas
2012-01-01
For a stochastic factor model we maximize the long-term growth rate of robust expected power utility with parameter $\\lambda\\in(0,1)$. Using duality methods the problem is reformulated as an infinite time horizon, risk-sensitive control problem. Our results characterize the optimal growth rate, an optimal long-term trading strategy and an asymptotic worst-case model in terms of an ergodic Bellman equation. With these results we propose a duality approach to a "robust large deviations" criterion for optimal long-term investment.
Asymptotics of Lagged Fibonacci Sequences
Mertens, Stephan
2009-01-01
Consider "lagged" Fibonacci sequences $a(n) = a(n-1)+a(\\lfloor n/k\\rfloor)$ for $k > 1$. We show that $\\lim_{n\\to\\infty} a(kn)/a(n)\\cdot\\ln n/n = k\\ln k$ and we demonstrate the slow numerical convergence to this limit and how to deal with this slow convergence. We also discuss the connection between two classical results of N.G. de Bruijn and K. Mahler on the asymptotics of $a(n)$.
Institute of Scientific and Technical Information of China (English)
孙孝前; 尤进红
2003-01-01
In this paper we consider the estimating problem of a semiparametric regression modelling whenthe data are longitudinal. An iterative weighted partial spline least squares estimator (IWPSLSE) for the para-metric component is proposed which is more efficient than the weighted partial spline least squares estimator(WPSLSE) with weights constructed by using the within-group partial spline least squares residuals in the senseof asymptotic variance. The asymptotic normality of this IWPSLSE is established. An adaptive procedure ispresented which ensures that the iterative process stops after a finite number of iterations and produces anestimator asymptotically equivalent to the best estimator that can be obtained by using the iterative proce-dure. These results are generalizations of those in heteroscedastic linear model to the case of semiparametric regression.
Extreme values and kernel estimates of point processes boundaries
Girard, Stéphane
2011-01-01
We present a method for estimating the edge of a two-dimensional bounded set, given a finite random set of points drawn from the interior. The estimator is based both on a Parzen-Rosenblatt kernel and extreme values of point processes. We give conditions for various kinds of convergence and asymptotic normality. We propose a method of reducing the negative bias and edge effects, illustrated by a simulation.
Fucci, D; Petrosino, L; Underwood, G; Clark, K
1992-10-01
The purpose of this study was to investigate differences in function of the tactile sensory system between groups of normal-speaking children and children with articulation problems. This task was accomplished by studying possible tactile threshold shifts occurring during magnitude-estimation scaling of vibratory stimuli presented to the dorsal surface of the tongue. 10 normal-speaking children (M age = 7.8 yr.) and 9 children with articulation problems (M age = 7.5 yr.) participated. The normal-speaking children and articulatory defective children performed differently on the magnitude-estimation scaling task in which threshold was allowed to return to baseline after each stimulus presentation. These two groups of children also showed dissimilar threshold shifts for the suprathreshold intensities employed in the magnitude-estimation scaling.
Directory of Open Access Journals (Sweden)
Syeda Refat Sultana
2014-01-01
Full Text Available For estimation of grain yield in wheat, Normalized Difference Vegetation Index (NDVI is considered as a potential screening tool. Field experiments were conducted to scrutinize the response of NDVI to yield behavior of different wheat cultivars and nitrogen fertilization at agronomic research area, University of Agriculture Faisalabad (UAF during the two years 2008-09 and 2009-10. For recording the value of NDVI, Green seeker (Handheld-505 was used. Split plot design was used as experimental model in, keeping four nitrogen rates (N1= 0 kg ha−1, N2= 55 kg ha−1, N3=110 kg ha−1, and N4= 220 kg ha−1 in main plots and ten wheat cultivars (Bakkhar-2001, Chakwal-50, Chakwal-97, Faisalabad-2008, GA-2002, Inqlab-91, Lasani-2008, Miraj-2008, Sahar-2006, and Shafaq-2006 in subplots with four replications. Impact of nitrogen and difference between cultivars were forecasted through NDVI. The results suggested that nitrogen treatment N4 (220 kg ha−1 and cultivar Faisalabad-2008 gave maximum NDVI value (0.85 at grain filling stage among all treatments. The correlation among NDVI at booting, grain filling, and maturity stages with grain yield was positive (R2 = 0.90; R2 = 0.90; R2 = 0.95, respectively. So, booting, grain filling, and maturity can be good depictive stages during mid and later growth stages of wheat crop under agroclimatic conditions of Faisalabad and under similar other wheat growing environments in the country.
Directory of Open Access Journals (Sweden)
R. Fares
2012-01-01
Full Text Available We study the nonsteady Stokes flow in a thin tube structure composed by two thin rectangles with lateral elastic boundaries which are connected by a domain with rigid boundaries. After a variational approach of the problem which gives us existence, uniqueness, regularity results, and some a priori estimates, we construct an asymptotic solution. The existence of a junction region between the two rectangles imposes to consider, as part of the asymptotic solution, some boundary layer correctors that correspond to this region. We present and solve the problems for all the terms of the asymptotic expansion. For two different cases, we describe the order of steps of the algorithm of solving the problem and we construct the main term of the asymptotic expansion. By means of the a priori estimates, we justify our asymptotic construction, by obtaining a small error between the exact and the asymptotic solutions.
Asymptotically Free Gauge Theories. I
Wilczek, Frank; Gross, David J.
1973-07-01
Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization group techniques and their application to scaling phenomena. The renormalization group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large space-like momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3)xSU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of non-color singlet physical states. The deep inelastic structure functions, as well as the electron position total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive lightcone or parton model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.
Asymptotic safety goes on shell
Benedetti, Dario
2011-01-01
It is well known in quantum field theory that the off-shell effective action depends on the gauge choice and field parametrization used in calculating it. Nevertheless, the typical scheme in which the scenario of asymptotically safe gravity is investigated is an off-shell version of the functional renormalization group equation. Working with the Einstein-Hilbert truncation as a test bed, we develop a new scheme for the analysis of asymptotically safe gravity in which the on-shell part of the effective action is singled out and we show that the beta function for the essential coupling has no explicit gauge-dependence. In order to reach our goal, we introduce several technical novelties, including a different decomposition of the metric fluctuations, a new implementation of the ghost sector, and a new cut-off scheme. We find a non-trivial fixed point, with a value of the cosmological constant which is independent of the gauge-fixing parameters.
Institute of Scientific and Technical Information of China (English)
2009-01-01
In this paper, we study the local asymptotic behavior of the regression spline estimator in the framework of marginal semiparametric model. Similarly to Zhu, Fung and He (2008), we give explicit expression for the asymptotic bias of regression spline estimator for nonparametric function f. Our results also show that the asymptotic bias of the regression spline estimator does not depend on the working covariance matrix, which distinguishes the regression splines from the smoothing splines and the seemingly unrelated kernel. To understand the local bias result of the regression spline estimator, we show that the regression spline estimator can be obtained iteratively by applying the standard weighted least squares regression spline estimator to pseudo-observations. At each iteration, the bias of the estimator is unchanged and only the variance is updated.
ASYMPTOTIC THEORY OF INITIAL VALUE PROBLEMS FOR NONLINEAR PERTURBED KLEIN-GORDON EQUATIONS
Institute of Scientific and Technical Information of China (English)
GAN Zai-hui; ZHANG Jian
2005-01-01
The asymptotic theory of initial value problems for a class of nonlinear perturbed Klein-Gordon equations in two space dimensions is considered. Firstly, using the contraction mapping principle, combining some priori estimates and the convergence of Bessel function, the well-posedness of solutions of the initial value problem in twice continuous differentiable space was obtained according to the equivalent integral equation of initial value problem for the Klein-Gordon equations. Next, formal approximations of initial value problem was constructed by perturbation method and the asymptotic validity of the formal approximation is got. Finally, an application of the asymptotic theory was given, the asymptotic approximation degree of solutions for the initial value problem of a specific nonlinear Klein-Gordon equation was analyzed by using the asymptotic approximation theorem.
Asymptotic properties of the C-Metric
Sladek, Pavel
2010-01-01
The aim of this article is to analyze the asymptotic properties of the C-metric, using a general method specified in work of Tafel and coworkers, [1], [2], [3]. By finding an appropriate conformal factor $\\Omega$, it allows the investigation of the asymptotic properties of a given asymptotically flat spacetime. The news function and Bondi mass aspect are computed, their general properties are analyzed, as well as the small mass, small acceleration, small and large Bondi time limits.
An estimating function approach to inference for inhomogeneous Neyman-Scott processes
DEFF Research Database (Denmark)
Waagepetersen, Rasmus Plenge
“This paper is concerned with inference for a certain class of inhomogeneous Neyman-Scott point processes depending on spatial covariates. Regression parameter estimates obtained from a simple estimating function are shown to be asymptotically normal when the “mother” intensity for the Neyman-Sco......-Scott process tends to infinity. Clustering parameter estimates are obtained using minimum contrast estimation based on the K-function. The approach is motivated and illustrated by applications to point pattern data from a tropical rain forest plot.......“This paper is concerned with inference for a certain class of inhomogeneous Neyman-Scott point processes depending on spatial covariates. Regression parameter estimates obtained from a simple estimating function are shown to be asymptotically normal when the “mother” intensity for the Neyman...
Linearized asymptotic stability for fractional differential equations
Directory of Open Access Journals (Sweden)
Nguyen Cong
2016-06-01
Full Text Available We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization at the equilibrium is asymptotically stable. As a consequence we extend Lyapunov's first method to fractional differential equations by proving that if the spectrum of the linearization is contained in the sector $\\{\\lambda \\in \\mathbb{C} : |\\arg \\lambda| > \\frac{\\alpha \\pi}{2}\\}$ where $\\alpha > 0$ denotes the order of the fractional differential equation, then the equilibrium of the nonlinear fractional differential equation is asymptotically stable.
Supersymmetric asymptotic safety is not guaranteed
DEFF Research Database (Denmark)
Intriligator, Kenneth; Sannino, Francesco
2015-01-01
It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety...... in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those...
Variance estimators in critical branching processes with non-homogeneous immigration
Rahimov, Ibrahim
2012-01-01
The asymptotic normality of conditional least squares estimators for the offspring variance in critical branching processes with non-homogeneous immigration is established, under moment assumptions on both reproduction and immigration. The proofs use martingale techniques and weak convergence results in Skorokhod spaces.
Properties of Estimated Characteristic Roots
DEFF Research Database (Denmark)
Nielsen, Bent; Nielsen, Heino Bohn
Estimated characteristic roots in stationary autoregressions are shown to give rather noisy information about their population equivalents. This is remarkable given the central role of the characteristic roots in the theory of autoregressive processes. In the asymptotic analysis the problems appear...... when multiple roots are present as this imply a non-differentiability so the d-method does not apply, convergence rates are slow, and the asymptotic distribution is non-normal. In finite samples this has a considerable influence on the finite sample distribution unless the roots are far apart....... With increasing order of the autoregressions it becomes increasingly difficult to place the roots far apart giving a very noisy signal from the characteristic roots....
The asymptotic convergence factor for a polygon under a perturbation
Energy Technology Data Exchange (ETDEWEB)
Li, X. [Georgia Southern Univ., Statesboro, GA (United States)
1994-12-31
Let Ax = b be a large system of linear equations, where A {element_of} C{sup NxN}, nonsingular and b {element_of} C{sup N}. A few iterative methods for solving have recently been presented in the case where A is nonsymmetric. Many of their algorithms consist of two phases: Phase I: estimate the extreme eigenvalues of A; Phase II: construct and apply an iterative method based on the estimates. For convenience, it is rewritten as an equivalent fixed-point form, x = Tx + c. Let {Omega} be a compact set excluding 1 in the complex plane, and let its complement in the extended complex plane be simply connected. The asymptotic convergence factor (ACF) for {Omega}, denoted by {kappa}({Omega}), measures the rate of convergence for the asymptotically optimal semiiterative methods for solving, where {sigma}(T) {contained_in} {Omega}.
First-order asymptotic corrections to the meanfield limit
Energy Technology Data Exchange (ETDEWEB)
Christandl, Matthias [Institute for Theoretical Physics, ETH Zuerich, Wolfgang-Pauli-Strasse 27, CH-8093 Zuerich (Switzerland); Matjeschk, Robert; Werner, Reinhard [Leibniz Universitaet Hannover (Germany); Trimborn, Friederike [Leibniz Universitaet Hannover (Germany); Bundesministerium fuer Bildung und Forschung (Germany)
2014-07-01
We derive a complete algebraic theory for treating permutation invariant problems beyond separability to first order in the asymptotics. Our work builds on a C{sup *}-algebraic theory for permutation invariant operators on n-particles, with an algebraic description of the limit n→∞ (the mean-field limit). We use the fluctuation ansatz, a version of a non-commutative central limit, and derive a continuous-variable algebra (the fluctuation algebra) that asymptotically describes the 1/n-corrections to this meanfield limit. Using the fluctuation algebra, we derive a method for estimating the ground-state energy of mean-field models up to first order, and for estimating the time-evolution of correlations between different particles. Moreover, we show that the mean-field ground-state problem is closely related to the finite de Finetti problem and therefore obtain a lower bound, complementing recent results in this direction.
Asymptotic Analysis of Mixed Modes in Red Giant Stars
Jiang, C
2014-01-01
High precision space observations, such as made by the kepler and corot missions, allow us to detect mixed modes for $l = 1$ modes in their high signal-to-noise photometry data. By means of asteroseismology, the inner structure of red giant (RG) stars is revealed the first time with the help of mixed modes. We analyse these mixed modes of a 1.3 $M_{sun}$ RG model theoretically from the approximate asymptotic descriptions of oscillations. While fitting observed frequencies with the eigenvalue condition for mixed modes, a good estimate of period spacing and coupling strength is also acquired for more evolved models. We show that the behaviour of the mode inertia in a given mode varies dramatically when the coupling is strong. An approximation of period spacings is also obtained from the asymptotic dispersion relation, which provides a good estimate of the coupling strength as well as period spacing when g-mode-like mixed modes are sufficiently dense.
Applications of Asymptotic Sampling on High Dimensional Structural Dynamic Problems
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Bucher, Christian
2011-01-01
is minimized. Next, the method is applied on different cases of linear and nonlinear systems with a large number of random variables representing the dynamic excitation. The results show that asymptotic sampling is capable of providing good approximations of low failure probability events for very high......The paper represents application of the asymptotic sampling on various structural models subjected to random excitations. A detailed study on the effect of different distributions of the so-called support points is performed. This study shows that the distribution of the support points has...... considerable effect on the final estimations of the method, in particular on the coefficient of variation of the estimated failure probability. Based on these observations, a simple optimization algorithm is proposed which distributes the support points so that the coefficient of variation of the method...
Applications of Asymptotic Sampling on High Dimensional Structural Dynamic Problems
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Bucher, Christian
2011-01-01
is minimized. Next, the method is applied on different cases of linear and nonlinear systems with a large number of random variables representing the dynamic excitation. The results show that asymptotic sampling is capable of providing good approximations of low failure probability events for very high......The paper represents application of the asymptotic sampling on various structural models subjected to random excitations. A detailed study on the effect of different distributions of the so-called support points is performed. This study shows that the distribution of the support points has...... considerable effect on the final estimations of the method, in particular on the coefficient of variation of the estimated failure probability. Based on these observations, a simple optimization algorithm is proposed which distributes the support points so that the coefficient of variation of the method...
Asymptotic properties for the semiparametric regression model with randomly censored data
Institute of Scientific and Technical Information of China (English)
王启华; 郑忠国
1997-01-01
Suppose that the patients’ survival times,Y,are random variables following the semiparametric regression model Y=Xβ+g(T)+ε,where (X,T) is a radom vector taking values in R×[0,1],β is an unknown parameter,g(·) is an unknown smooth regression function and εis the random error with zero mean and variance σ2.It is assumed that (X,T) is independent of ε.The estimators βn and gm(·) ofβ and g(·) are defined,respectively,when the observations are randomly censored on the right and the censoring distribution is unknown.Moreover,it isshown that βm is asymptotically normal and gm(·) is weak consistence with rate Op(n-1/3).
Variational approach for spatial point process intensity estimation
DEFF Research Database (Denmark)
Coeurjolly, Jean-Francois; Møller, Jesper
We introduce a new variational estimator for the intensity function of an inhomogeneous spatial point process with points in the d-dimensional Euclidean space and observed within a bounded region. The variational estimator applies in a simple and general setting when the intensity function...... is assumed to be of log-linear form β+θ⊤z(u) where z is a spatial covariate function and the focus is on estimating θ. The variational estimator is very simple to implement and quicker than alternative estimation procedures. We establish its strong consistency and asymptotic normality. We also discuss its...
A KERNEL-TYPE ESTIMATOR OF A QUANTILE FUNCTION UNDER RANDOMLY TRUNCATED DATA
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A kernel-type estimator of the quantile function Q(p) = inf{t: F(t) ≥ p},0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations of the kernel smooth estimator are established, and from Bahadur representations the authors can show that this estimator is strongly consistent, asymptotically normal, and weakly convergent.
A GLOBALLY UNIFORM ASYMPTOTIC EXPANSION OF THE HERMITE POLYNOMIALS
Institute of Scientific and Technical Information of China (English)
Shi Wei
2008-01-01
In this article, the author extends the validity of a uniform asymptotic ex-pansion of the Hermite polynomials HN(√2n+1α) to include all positive values of a.His method makes use of the rational functions introduced by Olde Daalhuis and Temme (SIAM J. Math. Anal., (1994), 25: 304-321). A new estimate for the remainder is given.
Stahel-Donoho kernel estimation for fixed design nonparametric regression models
Institute of Scientific and Technical Information of China (English)
LIN; Lu
2006-01-01
This paper reports a robust kernel estimation for fixed design nonparametric regression models.A Stahel-Donoho kernel estimation is introduced,in which the weight functions depend on both the depths of data and the distances between the design points and the estimation points.Based on a local approximation,a computational technique is given to approximate to the incomputable depths of the errors.As a result the new estimator is computationally efficient.The proposed estimator attains a high breakdown point and has perfect asymptotic behaviors such as the asymptotic normality and convergence in the mean squared error.Unlike the depth-weighted estimator for parametric regression models,this depth-weighted nonparametric estimator has a simple variance structure and then we can compare its efficiency with the original one.Some simulations show that the new method can smooth the regression estimation and achieve some desirable balances between robustness and efficiency.
Kalayeh, H. M.; Landgrebe, D. A.
1983-01-01
A criterion which measures the quality of the estimate of the covariance matrix of a multivariate normal distribution is developed. Based on this criterion, the necessary number of training samples is predicted. Experimental results which are used as a guide for determining the number of training samples are included. Previously announced in STAR as N82-28109
DEFF Research Database (Denmark)
Mocroft, Amanda; Lundgren, Jens D; Ross, Michael
2016-01-01
of exposure to antiretrovirals and the development of chronic kidney disease in people with initially normal renal function, as measured by estimated glomerular filtration rate (eGFR). METHODS: In this prospective international cohort study, HIV-positive adult participants (aged ≥16 years) from the D...
Involatile nanodroplets: an asymptotic analysis.
Jarymowycz, Lucien B; Ortoleva, Peter J
2006-06-21
The structure of nanometer-scale droplets of weakly volatile liquids arises through the interplay of strong intermolecular attraction, and core intermolecular repulsion, interfacial forces, and the large, negative chemical potential of the low density vapor with which it is in equilibrium. Using a van der Waals equation of state and a mesoscopic multiphase model, the structure of such nanodroplets is determined via an asymptotic analysis in terms of the ambient to critical temperature ratio. The structure of a spherical droplet is obtained as the solution of a simple "shooting" problem. The intradroplet pressure profile and a minimal droplet size are determined. The high pressure in the core of the droplet gives evidence for the preferred melting there for systems like water with a negative volume of melting. Our methodology can be generalized to multiphase droplets, as well as to composite structures wherein viruses or other nanoparticles are embedded.
Asymptotic expansions in nonlinear rotordynamics
Day, William B.
1987-01-01
This paper is an examination of special nonlinearities of the Jeffcott equations in rotordynamics. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot-firing ground testing. Deadband, side force, and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency, is defined and used to develop the solutions of the nonlinear Jeffcott equations as singular asymptotic expansions. This nonlinear natural frequency, which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies.
Asymptotic analysis of laminated plates and shallow shells
Skoptsov, K. A.; Sheshenin, S. V.
2011-02-01
It was noted long ago [1] that the material strength theory develops both by improving computational methods and by widening the physical foundations. In the present paper, we develop a computational technique based on asymptotic methods, first of all, on the homogenization method [2, 3]. A modification of the homogenization method for plates periodic in the horizontal projection was proposed in [4], where the bending of a homogeneous plate with periodically repeating inhomogeneities on its surface was studied. A more detailed asymptotic analysis of elastic plates periodic in the horizontal projection can be found, e.g., in [5, 6]. In [6], three asymptotic approximations were considered, local problems on the periodicity cell were obtained for them, and the solvability of these problems was proved. In [7], it was shown that the techniques developed for plates periodic in the horizontal projection can also be used for laminated plates. In [7], this was illustrated by an example of asymptotic analysis of an isotropic plate symmetric with respect to the midplane. In what follows, these methods are generalized to the case of combined bending and extension of a longitudinal laminated plate up to the third approximation, which permits finding all components of the stress tensor. The study of the plate behavior is based on the method of homogenization of the three-dimensional problem of linear elasticity and does not use any hypotheses. It turns out that the Kirchhoff-Love hypothesis for the entire packet of layers is simply a consequence of the method in the zeroth approximation, and the bending stresses corresponding to the classical theory of laminated plates [8] are obtained in the first approximation. The successive approximations describe the behavior of the normal and the stress more precisely. In the present paper, the results obtained in [7] are refined, and the asymptotic solution is compared with the direct analysis of a laminated plate by the finite
Nikitenko, Yaroslav
2015-01-01
The directional precision of the sample mean estimator was calculated analytically for the offset exponential and normal distributions in three-dimensional space both for a finite sample and for limiting cases. It was shown that the spherical projection of the sample mean of the shifted exponential distribution has connections with modified Bessel functions and with hypergeometric functions. It was shown explicitly how the distribution of the sample mean of the exponential pdf converges near the mode to the normal distribution. Approximation formulae for the distribution of the sample mean of the shifted exponential distribution and for its directional precision and for the precision of the estimation of the direction of shift of the normal distribution were obtained.
Einstein Constraints on Asymptotically Euclidean Manifolds
Choquet-Bruhat, Y; York, J W; Choquet-Bruhat, Yvonne; Isenberg, James; York, James W.
2000-01-01
We consider the Einstein constraints on asymptotically euclidean manifolds $M$ of dimension $n \\geq 3$ with sources of both scaled and unscaled types. We extend to asymptotically euclidean manifolds the constructive method of proof of existence. We also treat discontinuous scaled sources. In the last section we obtain new results in the case of non-constant mean curvature.
PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS
Institute of Scientific and Technical Information of China (English)
FEIGUIHUA; QIUQINGJIU
1997-01-01
The authors establish the existence of nontrival periodic solutions of the asymptotically linear Hamiltomian systems in the general case that the asymptotic matrix may be degenerate and time-dependent.This is done by using the critical point theory,Galerkin approximation procedure and the Maslov-type index theory introduced and generalized by Conley,Zehnder and Long.
Term structure modeling and asymptotic long rate
Yao, Y.
1999-01-01
This paper examines the dynamics of the asymptotic long rate in three classes of term structure models. It shows that, in a frictionless and arbitrage-free market, the asymptotic long rate is a non-decreasing process. This gives an alternative proof of the same result of Dybvig et al. (Dybvig, P.H.,
Asymptotic Spreading Fastened by Inter-Specific Coupled Nonlinearities: a Cooperative System
Lin, Guo
2010-01-01
This paper is concerned with the asymptotic spreading of a Lotka-Volterra cooperative system. Utilizing the theory developed by Berestycki et al. [Asymptotic spreading in heterogeneous diffusive excitable media, J. Funct. Anal. \\textbf{255} (2008), 2146-2189] for nonautonomous scalar equations, the lower bounds of spreading speeds of unknown functions formulated by a coupled system are estimated. Our results imply that the asymptotic spreading of one species can be significantly fastened by introducing a mutual species, which indicates the role of cooperation described by the coupled nonlinearities.
Bulcock, J. W.; And Others
Multicollinearity refers to the presence of highly intercorrelated independent variables in structural equation models, that is, models estimated by using techniques such as least squares regression and maximum likelihood. There is a problem of multicollinearity in both the natural and social sciences where theory formulation and estimation is in…
Asymptotic properties of random matrices and pseudomatrices
Lenczewski, Romuald
2010-01-01
We study the asymptotics of sums of matricially free random variables called random pseudomatrices, and we compare it with that of random matrices with block-identical variances. For objects of both types we find the limit joint distributions of blocks and give their Hilbert space realizations, using operators called `matricially free Gaussian operators'. In particular, if the variance matrices are symmetric, the asymptotics of symmetric blocks of random pseudomatrices agrees with that of symmetric random blocks. We also show that blocks of random pseudomatrices are `asymptotically matricially free' whereas the corresponding symmetric random blocks are `asymptotically symmetrically matricially free', where symmetric matricial freeness is obtained from matricial freeness by an operation of symmetrization. Finally, we show that row blocks of square, lower-block-triangular and block-diagonal pseudomatrices are asymptotically free, monotone independent and boolean independent, respectively.
Universal asymptotic umbrella for hydraulic fracture modeling
Linkov, Aleksandr M
2014-01-01
The paper presents universal asymptotic solution needed for efficient modeling of hydraulic fractures. We show that when neglecting the lag, there is universal asymptotic equation for the near-front opening. It appears that apart from the mechanical properties of fluid and rock, the asymptotic opening depends merely on the local speed of fracture propagation. This implies that, on one hand, the global problem is ill-posed, when trying to solve it as a boundary value problem under a fixed position of the front. On the other hand, when properly used, the universal asymptotics drastically facilitates solving hydraulic fracture problems (both analytically and numerically). We derive simple universal asymptotics and comment on their employment for efficient numerical simulation of hydraulic fractures, in particular, by well-established Level Set and Fast Marching Methods.
Directory of Open Access Journals (Sweden)
Gavilá́n Ruiz, José́ Manuel
2011-06-01
Full Text Available El uso del método de máxima verosimilitud para estimar modelos de producción Half-Normal con frontera estocástica conlleva algunas dificultades prácticas que tal vez no han sido suficientemente enfatizadas. Usando el software FRONTIER, analizamos el caso en que la estimación sugiere la ausencia de factores aleatorios en el término de error compuesto. Hemos comprobado que existen motivos para pensar que las estimaciones de los parámetros y, sobre todo, sus errores estándar son de dudosa validez. El software LIMDEP no obtiene estimaciones en este caso, ofreciendo un mensaje de error. || Using the maximum likelihood method, in order to estimate Half-Normal stochastic frontier production models, entails several practical difficulties that, perhaps, have not been sufficiently emphasised. In employing FRONTIER software, we analyse the case in which the estimation obtained suggests the absence of random factors in the composite error term. We have proved that there are reasons to doubt the validity of the parameter estimates and especially of its standard errors. On the other hand, no estimation is obtained in the previous situation, with LIMDEP software, but an error message.
TIME-ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR GENERAL NAVIER-STOKES EQUATIONS IN EVEN SPACE-DIMENSION
Institute of Scientific and Technical Information of China (English)
Xu Hongmei
2001-01-01
We study the time-asymptotic behavior of solutions to general NavierStokes equations in even and higher than two space-dimensions. Through the pointwise estimates of the Green function of the linearized system, we obtain explicit expressions of the time-asymptotic behavior of the solutions. The result coincides with weak Huygan's principle.
The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere
Brauchart, J S; Saff, E B
2012-01-01
We survey known results and present estimates and conjectures for the next-order term in the asymptotics of the optimal logarithmic energy and Riesz $s$-energy of $N$ points on the unit sphere in $\\mathbb{R}^{d+1}$, $d\\geq 1$. The conjectures are based on analytic continuation assumptions (with respect to $s$) for the coefficients in the asymptotic expansion (as $N\\to \\infty$) of the optimal $s$-energy.
Asymptotics for the greatest zeros of solutions of a particular O.D.E.
Directory of Open Access Journals (Sweden)
Silvia Noschese
1994-05-01
Full Text Available This paper deals with the Liouville-Stekeloff method for approximating solutions of homogeneous linear ODE and a general result due to Tricomi which provides estimates for the zeros of functions by means of the knowledge of an asymptotic representation. From the classical tools we deduce information about the asymptotics of the greatest zeros of a class of solutions of a particular ODE, including the classical Hermite polynomials.
Asymptotic Solutions of Serial Radial Fuel Shuffling
Directory of Open Access Journals (Sweden)
Xue-Nong Chen
2015-12-01
Full Text Available In this paper, the mechanism of traveling wave reactors (TWRs is investigated from the mathematical physics point of view, in which a stationary fission wave is formed by radial fuel drifting. A two dimensional cylindrically symmetric core is considered and the fuel is assumed to drift radially according to a continuous fuel shuffling scheme. A one-group diffusion equation with burn-up dependent macroscopic coefficients is set up. The burn-up dependent macroscopic coefficients were assumed to be known as functions of neutron fluence. By introducing the effective multiplication factor keff, a nonlinear eigenvalue problem is formulated. The 1-D stationary cylindrical coordinate problem can be solved successively by analytical and numerical integrations for associated eigenvalues keff. Two representative 1-D examples are shown for inward and outward fuel drifting motions, respectively. The inward fuel drifting has a higher keff than the outward one. The 2-D eigenvalue problem has to be solved by a more complicated method, namely a pseudo time stepping iteration scheme. Its 2-D asymptotic solutions are obtained together with certain eigenvalues keff for several fuel inward drifting speeds. Distributions of the neutron flux, the neutron fluence, the infinity multiplication factor kinf and the normalized power are presented for two different drifting speeds.
A note on constrained M-estimation and its recursive analog in multivariate linear regression models
Institute of Scientific and Technical Information of China (English)
RAO; Calyampudi; R
2009-01-01
In this paper,the constrained M-estimation of the regression coeffcients and scatter parameters in a general multivariate linear regression model is considered.Since the constrained M-estimation is not easy to compute,an up-dating recursion procedure is proposed to simplify the com-putation of the estimators when a new observation is obtained.We show that,under mild conditions,the recursion estimates are strongly consistent.In addition,the asymptotic normality of the recursive constrained M-estimators of regression coeffcients is established.A Monte Carlo simulation study of the recursion estimates is also provided.Besides,robustness and asymptotic behavior of constrained M-estimators are briefly discussed.
Double robust estimator of average causal treatment effect for censored medical cost data.
Wang, Xuan; Beste, Lauren A; Maier, Marissa M; Zhou, Xiao-Hua
2016-08-15
In observational studies, estimation of average causal treatment effect on a patient's response should adjust for confounders that are associated with both treatment exposure and response. In addition, the response, such as medical cost, may have incomplete follow-up. In this article, a double robust estimator is proposed for average causal treatment effect for right censored medical cost data. The estimator is double robust in the sense that it remains consistent when either the model for the treatment assignment or the regression model for the response is correctly specified. Double robust estimators increase the likelihood the results will represent a valid inference. Asymptotic normality is obtained for the proposed estimator, and an estimator for the asymptotic variance is also derived. Simulation studies show good finite sample performance of the proposed estimator and a real data analysis using the proposed method is provided as illustration. Copyright © 2016 John Wiley & Sons, Ltd.
Charnotskii, Mikhail; Baker, Gary J.
2011-06-01
Asymptotic theory of the finite beam scintillations (Charnotskii, WRM, 1994, JOSA A, 2010) provides an exhaustive description of the dependence of the beam scintillation index on the propagation conditions, beam size and focusing. However the complexity of the asymptotic configuration makes it difficult to apply these results for the practical calculations of the scintillation index (SI). We propose an estimation technique and demonstrate some examples of the calculations of the scintillation index dependence on the propagation path length, initial beam size, wavelength and turbulence strength for the beam geometries and propagation scenarios that are typical for applications. We suggest simple analytic bridging approximations that connect the specific asymptotes with the accuracy sufficient for the engineering estimates. Proposed technique covers propagation of the wide, narrow, collimated and focused beams under the weak and strong scintillation conditions. Direct numeric simulation of the beam waves propagation through turbulence expediently complements the asymptotic theory being most efficient when the governing scales difference is not very large. We performed numerical simulations of the beam wave propagation through turbulence for conditions that partially overlap with the major parameter space domains of the asymptotic theory. The results of the numeric simulation are used to confirm the asymptotic theory and estimate the accuracy of the bridging approximations.
Asymptotic Formulas for Thermography Based Recovery of Anomalies
Institute of Scientific and Technical Information of China (English)
Habib Ammari; Anastasia Kozhemyak; Darko Volkov
2009-01-01
We start from a realistic half space model for thermal imaging, which we then use to develop a mathematical asymptotic analysis well suited for the design of reconstruction algorithms. We seek to reconstruct thermal anomalies only through their rough features. With this way our proposed algorithms are stable against measurement noise and geometry perturbations. Based on rigorous asymptotic estimates, we first obtain an approximation for the temperature profile which we then use to design nonit-erative detection algorithms. We show on numerical simulations evidence that they are accurate and robust. Moreover, we provide a mathematical model for ultrasonic temperature imaging, which is an important technique in cancerous tissue ablation therapy.AMS subject classifications: 35R20, 35B30
Asymptotic analysis of multicell massive MIMO over Rician fading channels
Sanguinetti, Luca
2017-06-20
This work considers the downlink of a multicell massive MIMO system in which L base stations (BSs) of N antennas each communicate with K single-antenna user equipments randomly positioned in the coverage area. Within this setting, we are interested in evaluating the sum rate of the system when MRT and RZF are employed under the assumption that each intracell link forms a MIMO Rician uncorrelated fading channel. The analysis is conducted assuming that N and K grow large with a non-trivial ratio N/K under the assumption that the data transmission in each cell is affected by channel estimation errors, pilot contamination, and an arbitrary large scale attenuation. Numerical results are used to validate the asymptotic analysis in the finite system regime and to evaluate the network performance under different settings. The asymptotic results are also instrumental to get insights into the interplay among system parameters.
Asymptotics of thermal spectral functions
Caron-Huot, S
2009-01-01
We use operator product expansion (OPE) techniques to study the spectral functions of currents at finite temperature, in the high-energy time-like region $\\omega\\gg T$. The leading corrections to the spectral function of currents and stress tensors are proportional to $\\sim T^4$ expectation values in general, and the leading corrections $\\sim g^2T^4$ are calculated at weak coupling, up to one undetermined coefficient in the shear viscosity channel. Spectral functions in the asymptotic regime are shown to be infrared safe up to order $g^8T^4$. The convergence of sum rules in the shear and bulk viscosity channels is established in QCD to all orders in perturbation theory, though numerically significant tails $\\sim T^4/(\\log\\omega)^3$ are shown to exist in the bulk viscosity channel and to have an impact on sum rules recently proposed by Kharzeev and Tuchin. We argue that the spectral functions of currents and stress tensors in strongly coupled $\\mathcal{N}=4$ super Yang-Mills do not receive any medium-dependent...
Asymptotics of Simple Branching Populations
Huillet, Thierry; Kłopotowski, Andrzej; Porzio, Anna
1995-09-01
In this paper we study a simple deterministic tree structure: an initial individual generates a finite number of offspring, each of which has given integer valued lifetime, iterating the same procedure when dying. Three asymptotic distributions of this asynchronous deterministic branching procedure are considered: the generation distribution, the ability of individuals to generate offspring and the age distribution. Thermodynamic formalism is then developped to reveal the multifractal nature of the mass splitting associated to our process. On considère l'itération d'une structure déterministe arborescente selon laquelle un ancêtre engendre un nombre fini de descendants dont la durée de vie (à valeurs entières) est donnée. Dans un premier temps on s'intéresse aux trois distributions asymptotiques suivantes : répartition des générations, aptitude à engendrer des descendants et répartition selon l'âge. Ensuite nous développons le formalisme thermodynamique pour mettre en évidence le caractère multifractal de la scission d'une masse unitaire associée à cette arborescence.
Institute of Scientific and Technical Information of China (English)
张金艳; 郭鹏江
2010-01-01
研究最近邻密度估计在两两NQD序列情形下的渐近正态性.在适当的条件下,以两两NQR序列的中心极限定理为基础证明相关结论.在相依情形下对最近邻密度估计的渐近正态性给予了证明.推广了独立同分布和其他相依情形下最近邻密度估计的大样本性质.
强混合序列的方差估计%ESTIMATION OF THE VARIANCE FOR STRONGLY MIXING SEQUENCES
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Let {X\\-n,n≥1} be a stationary strongly mixing random sequence satisfying EX1=μ,EX21＜∞ and (VarS\\-n)/n→σ2 as n→∞. In this paper a class of estimators of VarSn is studied. The weak consistency and asymptotic normality as well as the central limit theorem are presented.
DEFF Research Database (Denmark)
Jepsen, Morten Løve; Dau, Torsten
To partly characterize the function of cochlear processing in humans, the basilar membrane (BM) input-output function can be estimated. In recent studies, forward masking has been used to estimate BM compression. If an on-frequency masker is processed compressively, while an off-frequency masker...... processing at medium levels. If a signal can be masked by a low-level on-frequency masker such that signal and masker fall in the linear region of the I/O-function, then a steeper GOM function is expected. The knee-point can then be estimated in the input level region where the GOM changes significantly...... higher input levels and compression was similar to that of NH listeners....
Bias-reduced estimation of long memory stochastic volatility
DEFF Research Database (Denmark)
Frederiksen, Per; Nielsen, Morten Ørregaard
We propose to use a variant of the local polynomial Whittle estimator to estimate the memory parameter in volatility for long memory stochastic volatility models with potential nonstation- arity in the volatility process. We show that the estimator is asymptotically normal and capable of obtaining...... bias reduction as well as a rate of convergence arbitrarily close to the parametric rate, n1=2. A Monte Carlo study is conducted to support the theoretical results, and an analysis of daily exchange rates demonstrates the empirical usefulness of the estimators....
Institute of Scientific and Technical Information of China (English)
曾六川
2003-01-01
A new class of almost asymptotically nonexpansive type mappings in Banach spaces is introduced, which includes a number of known classes of nonlinear Lipschitzian mappings and non-Lipschitzian mappings in Banach spaces as special cases; for example,the known classes of nonexpansive mappings, asymptotically nonexpansive mappings and asymptotically nonexpansive type mappings. The convergence problem of modified Ishikawa iterative sequences with errors for approximating fixed points of almost asymptotically nonexpansive type mappings is considered. Not only S. S. Chang' s inequality but also H.K. Xu' s one for the norms of Banach spaces are applied to make the error estimate between the exact fixed point and the approximate one. Moreover, Zhang Shi-sheng ' s method (Applied Mathematics and Mechanics ( English Edition ), 2001,22 (1) :25 - 34) for making the convergence analysis of modified Ishikawa iterative sequences with errors is extended to the case of almost asymptotically nonexpansive type mappings. The new convergence criteria of modified Ishikawa iterative sequences with errors for finding fixed points of almost asymptotically nonexpansive type mappings in uniformly convex Banach spaces are presented. Also, the new convergence criteria of modified Mann iterative sequences with errors for this class of mappings are immediately obtained from these criteria. The above results unify, improve and generalize Zhang Shi-sheng's ones on approximating fixed points of asymptotically nonexpansive type mappings by the modified Ishikawa and Mann iterative sequences with errors.
Asymptotic Safety, Emergence and Minimal Length
Percacci, R
2010-01-01
There seems to be a common prejudice that asymptotic safety is either incompatible with, or at best unrelated to, the other topics in the title. This is not the case. In fact, we show that 1) the existence of a fixed point with suitable properties is a promising way of deriving emergent properties of gravity, and 2) there is a precise sense in which asymptotic safety implies a minimal length. In so doing we also discuss possible signatures of asymptotic safety in scattering experiments.
ASYMPTOTIC STABILITIES OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
SHEN Yi; JIANG Ming-hui; LIAO Xiao-xin
2006-01-01
Asymptotic characteristic of solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Lyapunov functions for locating the limit set of t he solution. Moreover, from them many effective criteria on stochastic asymptotic stability, which enable us to construct the Lyapunov functions much more easily in application, were obtained. The results show that the wellknown classical theorem on stochastic asymptotic stability is a special case of our more general results. In the end, application in stochastic Hopfield neural networks is given to verify our results.
Střelec, Luboš; Stehlík, Milan
2017-01-01
Normality of the error terms in regression models is one of the basic assumptions in the applied regression analysis. Therefore, testing for normality of the error terms constitutes one of the most important steps of regression model verification and validation. Failure to assess non-normality of the error terms may lead to incorrect results of usual statistical inference techniques such as t-test or F-test. Within the applied regression analysis there is a frequent problem of the presence of autocorrelation and conditional heteroscedasticity of the error terms. Under both autocorrelation and heteroscedasticity, the usual OLS estimators are still unbiased, linear and asymptotically normally distributed, however, no longer have the minimum variance property among all linear unbiased estimators. Therefore, the aim of this paper is to present and discuss normality testing of the error terms with presence of autocorrelation and conditional heteroscedasticity. To explore the power of selected classical tests and robust tests for normality, we perform simulation study.
Yim, Ji-Hye; Yun, Jung Mi; Kim, Ji Young; Nam, Seon Young; Kim, Cha Soon
2017-07-25
Low-dose radiation has various biological effects such as adaptive responses, low-dose hypersensitivity, as well as beneficial effects. However, little is known about the particular proteins involved in these effects. Here, we sought to identify low-dose radiation-responsive phosphoproteins in normal fibroblast cells. We assessed genomic instability and proliferation of fibroblast cells after γ-irradiation by γ-H2AX foci and micronucleus formation analyses and BrdU incorporation assay, respectively. We screened fibroblast cells 8 h after low-dose (0.05 Gy) γ-irradiation using Phospho Explorer Antibody Microarray and validated two differentially expressed phosphoproteins using Western blotting. Cell proliferation proceeded normally in the absence of genomic instability after low-dose γ-irradiation. Phospho antibody microarray analysis and Western blotting revealed increased expression of two phosphoproteins, phospho-NFκB (Ser536) and phospho-P70S6K (Ser418), 8 h after low-dose radiation. Our findings suggest that low-dose radiation of normal fibroblast cells activates the expression of phospho-NFκB (Ser536) and phospho-P70S6K (Ser418) in the absence of genomic instability. Therefore, these proteins may be involved in DNA damage repair processes.
Asymptotic silence in loop quantum cosmology
Mielczarek, Jakub
2012-01-01
The state of asymptotic silence, characterized by causal disconnection of the space points, emerges from various approaches aiming to describe gravitational phenomena in the limit of large curvatures. In particular, such behavior was anticipated by Belinsky, Khalatnikov and Lifshitz (BKL) in their famous conjecture put forward in the early seventies of the last century. While the BKL conjecture is based on purely classical considerations, one can expect that asymptotic silence should have its quantum counterpart at the level of a more fundamental theory of quantum gravity, which is the relevant description of gravitational phenomena in the limit of large energy densities. Here, we summarize some recent results which give support to such a possibility. More precisely, we discuss occurrence of the asymptotic silence due to polymerization of space at the Planck scale, in the framework of loop quantum cosmology. In the discussed model, the state of asymptotic silence is realized at the energy density $\\rho = \\rho...
Nonsymmetric gravity does have acceptable global asymptotics
Cornish, N J
1994-01-01
"Reports of my death are greatly exaggerated" - Mark Twain. We consider the claim by Damour, Deser and McCarthy that nonsymmetric gravity theory has unacceptable global asymptotics. We explain why this claim is incorrect.
Asymptotic Evolution of Random Unitary Operations
Novotny, J; Jex, I
2009-01-01
We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits.
The Lorentzian proper vertex amplitude: Asymptotics
Engle, Jonathan; Zipfel, Antonia
2015-01-01
In previous work, the Lorentzian proper vertex amplitude for a spin-foam model of quantum gravity was derived. In the present work, the asymptotics of this amplitude are studied in the semi-classical limit. The starting point of the analysis is an expression for the amplitude as an action integral with action differing from that in the EPRL case by an extra `projector' term which scales linearly with spins only in the asymptotic limit. New tools are introduced to generalize stationary phase methods to this case. For the case of boundary data which can be glued to a non-degenerate Lorentzian 4-simplex, the asymptotic limit of the amplitude is shown to equal the single Feynman term, showing that the extra term in the asymptotics of the EPRL amplitude has been eliminated.
Hermite polynomials and quasi-classical asymptotics
Energy Technology Data Exchange (ETDEWEB)
Ali, S. Twareque, E-mail: twareque.ali@concordia.ca [Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8 (Canada); Engliš, Miroslav, E-mail: englis@math.cas.cz [Mathematics Institute, Silesian University in Opava, Na Rybníčku 1, 74601 Opava, Czech Republic and Mathematics Institute, Žitná 25, 11567 Prague 1 (Czech Republic)
2014-04-15
We study an unorthodox variant of the Berezin-Toeplitz type of quantization scheme, on a reproducing kernel Hilbert space generated by the real Hermite polynomials and work out the associated quasi-classical asymptotics.
EFFICIENT ESTIMATION OF FUNCTIONAL-COEFFICIENT REGRESSION MODELS WITH DIFFERENT SMOOTHING VARIABLES
Institute of Scientific and Technical Information of China (English)
Zhang Riquan; Li Guoying
2008-01-01
In this article, a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different co-efficient functions is defined. First step, by the local linear technique and the averaged method, the initial estimates of the coefficient functions are given. Second step, based on the initial estimates, the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure. The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions. Two simulated examples show that the procedure is effective.
The trouble with asymptotically safe inflation
Fang, Chao
2013-01-01
In this paper we investigate the perturbation theory of the asymptotically safe inflation and we find that all modes of gravitational waves perturbation become ghosts in order to achieve a large enough number of e-folds. Formally we can calculate the power spectrum of gravitational waves perturbation, but we find that it is negative. It indicates that there is serious trouble with the asymptotically safe inflation.
Identification and estimation of non-Gaussian structural vector autoregressions
DEFF Research Database (Denmark)
Lanne, Markku; Meitz, Mika; Saikkonen, Pentti
-Gaussian components is, without any additional restrictions, identified and leads to (essentially) unique impulse responses. We also introduce an identification scheme under which the maximum likelihood estimator of the non-Gaussian SVAR model is consistent and asymptotically normally distributed. As a consequence......, additional economic identifying restrictions can be tested. In an empirical application, we find a negative impact of a contractionary monetary policy shock on financial markets, and clearly reject the commonly employed recursive identifying restrictions....
Institute of Scientific and Technical Information of China (English)
Tao Hu; Heng-jian Cui; Xing-wei Tong
2009-01-01
This article considers a semiparametric varying-coefficient partially linear regression model with current status data. The semiparametric varying-coefficient partially linear regression model which is a gen-eralization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estima-tor for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are conducted to examine the small-sample properties of the proposed estimates and a real dataset is used to illustrate our approach.
Asymptotics of certain families of Higgs bundles in the Hitchin component
DEFF Research Database (Denmark)
Collier, Brian; Li, Qiongling
2017-01-01
of the Hermitian metric solving the Higgs bundle equations. This analysis is used to estimate the asymptotics of the corresponding family of flat connections as we scale the differentials by a real parameter. We consider Higgs fields that have only one holomorphic differential $q_n$ of degree $n$ or $q_{n-1......Using Hitchin's parameterization of the Hitchin-Teichm\\"uller component of the $SL(n,\\mathbb{R})$ representation variety, we study the asymptotics of certain families of representations. In fact, for certain Higgs bundles in the $SL(n,\\mathbb{R})$-Hitchin component, we study the asymptotics......}$ of degree $n-1.$ We also study the asymptotics of the associated family of equivariant harmonic maps to the symmetric space $SL(n,\\mathbb{R})/SO(n,\\mathbb{R})$ and relate it to recent work of Katzarkov, Noll, Pandit and Simpson....
Non-linear and signal energy optimal asymptotic filter design
Directory of Open Access Journals (Sweden)
Josef Hrusak
2003-10-01
Full Text Available The paper studies some connections between the main results of the well known Wiener-Kalman-Bucy stochastic approach to filtering problems based mainly on the linear stochastic estimation theory and emphasizing the optimality aspects of the achieved results and the classical deterministic frequency domain linear filters such as Chebyshev, Butterworth, Bessel, etc. A new non-stochastic but not necessarily deterministic (possibly non-linear alternative approach called asymptotic filtering based mainly on the concepts of signal power, signal energy and a system equivalence relation plays an important role in the presentation. Filtering error invariance and convergence aspects are emphasized in the approach. It is shown that introducing the signal power as the quantitative measure of energy dissipation makes it possible to achieve reasonable results from the optimality point of view as well. The property of structural energy dissipativeness is one of the most important and fundamental features of resulting filters. Therefore, it is natural to call them asymptotic filters. The notion of the asymptotic filter is carried in the paper as a proper tool in order to unify stochastic and non-stochastic, linear and nonlinear approaches to signal filtering.
Thode, Henry C
2002-01-01
Describes the selection, design, theory, and application of tests for normality. Covers robust estimation, test power, and univariate and multivariate normality. Contains tests ofr multivariate normality and coordinate-dependent and invariant approaches.
On the asymptotic distribution of an alternative measure of kurtosis
Directory of Open Access Journals (Sweden)
Kagba Suaray
2015-08-01
Full Text Available Pearson defined the fourth standardized moment of a symmetric distribution as its kurtosis. There has been much discussion in the literature concerning both the meaning of kurtosis, as well as the effectiveness of the classical sample kurtosis as a reliable measure of peakedness and tail weight. In this paper, we consider an alternative measure, developed by Crow and Siddiqui, used to describe kurtosis. Its value is calculated for a number of common distributions, and a derivation of its asymptotic distribution is given. Simulations follow, which reveal an interesting connection to the literature on the ratio of normal random variables.
Yarmukhamedov, R
2016-01-01
Asymptotic expressions for the radial and full wave functions of a three{body bound halo nuclear system with two charged particles in relative coordinates are obtained in explicit form, when the relative distance between two particles tends to infinity. The obtained asymptotic forms are applied to the analysis of the asymptotic behavior of the three-body (pn?) wave functions for the halo ($E^*=3.562$ MeV, $J^{\\pi}=0^+$, $T=1$) state of $^6$Li derived by D. Baye within the Lagrange-mesh method for two forms of the $\\alpha N$ -potential. The agreement between the calculated wave function and the asymptotic formula is excellent for distances up to 30 fm. Information about the values of the three-body asymptotic normalization functions is extracted. It is shown that the extracted values of the three-body asymptotic normalization function are sensitive to the form of the $\\alpha N$ -potential. The mirror symmetry is revealed for the three-body asymptotic normalization functions derived for the isobaric ($^6$He, $^...
Asymptotic Properties in Semiparametric Partially Linear Regression Models for Functional Data
Institute of Scientific and Technical Information of China (English)
Tao ZHANG
2013-01-01
We consider the semiparametric partially linear regression models with mean function xTβ+g(z),where X and z are functional data.The new estimators of β and g(z) are presented and some asymptotic results are given.The strong convergence rates of the proposed estimators are obtained.In our estimation,the observation number of each subject will be completely flexible.Some simulation study is conducted to investigate the finite sample performance of the proposed estimators.
DEFF Research Database (Denmark)
Maraldo, Maja V; Lundemann, Michael; Vogelius, Ivan R;
2015-01-01
INTRODUCTION: Reconstruction of radiotherapy (RT) performed decades ago is challenging, but is necessary to address dose-response questions from epidemiological data and may be relevant in re-irradiation scenarios. Here, a novel method to reconstruct extended and involved field RT for patients...... with Hodgkin lymphoma was used. MATERIALS AND METHODS: For 46 model patients, 29 organs at risk (OARs) were contoured and seven treatment fields reconstructed (mantle, mediastinal, right/left neck, right/left axillary, and spleen field). Extended and involved field RT were simulated by generating RT plans...... by superpositions of the seven individual fields. The mean (standard deviation) of the 46 individual mean organ doses were extracted as percent of prescribed dose for each field superposition. RESULTS: The estimated mean doses to the OARs from 17 field combinations were presented. The inter-patient variability...
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Liu, W. F.
2013-01-01
Estimation of extreme response and failure probability of structures subjected to ultimate design loads is essential for structural design of wind turbines according to the new standard IEC61400-1. This task is focused on in the present paper in virtue of probability density evolution method (PDEM......), which underlies the schemes of random vibration analysis and structural reliability assessment. The short-term rare failure probability of 5-mega-watt wind turbines, for illustrative purposes, in case of given mean wind speeds and turbulence levels is investigated through the scheme of extreme value...... distribution instead of any other approximate schemes of fitted distribution currently used in statistical extrapolation techniques. Besides, the comparative studies against the classical fitted distributions and the standard Monte Carlo techniques are carried out. Numerical results indicate that PDEM exhibits...
Estimation of Recurrence Risk After Normal (18)F-FDG PET/CT in Nonsmall-Cell Lung Cancer.
Pak, Kyoungjune; Kim, Seong-Jang; Koo, Phillip J; Chang, Samuel
2016-06-01
The authors aimed to assess the risk of recurrence in patients with nonsmall-cell lung cancer after surgery with no evidence of disease (NED) demonstrated on (18)F-fluorodeoxyglucose (FDG) positron emission tomography/computed tomography (PET/CT). A total of 140 subjects with adenocarcinoma or squamous cell carcinoma of the lung were included in this study. Patients had FDG PET/CT scans within a year after surgery between January 2007 and December 2014. Patients with PET/CT scans with NED were included. Following an NED PET/CT scan, recurrence or metastasis was found in 14 patients (10.0%), and deaths in 4 (2.9%) during a median follow-up of 636 days. Although the rates of recurrence or metastasis were very low, the risk for recurrence continuously increased after 600 days up to 0.03%. The risk was higher in patients with positive margin at surgery, lymphovascular invasion, N2 stage, and TNM stage III/IV. In conclusion, according to the smoothed hazard functions, there was a very low risk of recurrence until 600 days after normal (18)F-FDG PET scans. The risk was higher in patients with positive margin at surgery, lymphovascular invasion, N2 stage, and TNM stage III/IV.
AN ASYMPTOTIC ANALYSIS METHOD FOR THE LINEAR SHELL
Institute of Scientific and Technical Information of China (English)
李开泰; 张文岭; 黄艾香
2004-01-01
In this paper, using the formal approach of asymptotic expansion for linear elastic shell we can get each term uk successively. According this metnod the leading term u0 will be identified by an elliptic boundary value problem, other terms will be obtained by the algebraic operations without solving partial differential equations. We give the variational formulation for the leading term U(x) and construct an approximate solution UKT(x,ζ):=U(x)+Ⅱ1Uζ+Ⅱ2Uζ2,then we give the estimation.
Computation and Asymptotic Analysis in the Impact Problem
Institute of Scientific and Technical Information of China (English)
Lei Hou; Lin Qiu
2009-01-01
Non-linear numerical method is applied to solve the viscons-elastic-plastic material impact problem.The finite element simulation agrees with the celebrated European crash safety analysis.The complex material stress distribution in the large deformation has been obtained,when the impact happens.Also the posterior-estimate solver and asymptotic analysis have been used for the sensitive pre-stage deformation before the impact happening.This part of simulation is very interesting for the passive safety in automotive protection devices.It is an important part of the mathematical modelling.
Directory of Open Access Journals (Sweden)
Xinguo Hou
Full Text Available OBJECTIVE: To investigate the relationship between lipid profiles [including total cholesterol (TC, triglyceride (TG, low-density lipoprotein cholesterol (LDL-C and high-density lipoprotein cholesterol (HDL-C] and a mild decline in the estimated glomerular filtration rate (eGFR in subjects with normal serum lipid levels. DESIGN AND METHODS: In this study, we included 2647 participants who were ≥ 40 years old and had normal serum lipid levels. The Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI equation was used to estimate the GFR. A mildly reduced eGFR was defined as 60-90 mL/min/1.73 m(2. First, multiple linear regression analysis was used to estimate the association of lipid profiles with the eGFR. Then, the levels of each lipid component were divided into four groups, using the 25th, 50th and 75th percentiles as cut-off points. Finally, multiple logistic regression analysis was used to investigate the association of different lipid components with the risk of mildly reduced eGFR. RESULTS: In the group with a mildly reduced eGFR, TG and LDL-C levels were significantly increased, but HDL-C levels were significantly decreased. After adjusting for age, gender, body mass index (BMI, systolic blood pressure (SBP, glycated hemoglobin (HbA1c, smoking and drinking, only TC and TG were independently related to the eGFR. Additionally, only TG showed a linear relationship with an increased risk of a mildly reduced eGFR, with the highest quartile group (TG: 108-150 mg/dl [1.22-1.70 mmol/L] having a significantly increased risk after adjusting for the above factors. CONCLUSIONS: Triglyceride levels are closely associated with a mildly reduced eGFR in subjects with normal serum lipid levels. Dyslipidemia with lower TG levels could be used as new diagnostic criteria for subjects with mildly reduced renal function.
Institute of Scientific and Technical Information of China (English)
Huan-bin Liu; Liu-quan Sun; Li-xing Zhu
2005-01-01
Many survival studies record the times to two or more distinct failures on each subject. The failures may be events of different natures or may be repetitions of the same kind of event. In this article, we consider the regression analysis of such multivariate failure time data under the additive hazards model. Simple weighted estimating functions for the regression parameters are proposed, and asymptotic distribution theory of the resulting estimators are derived. In addition, a class of generalized Wald and generalized score statistics for hypothesis testing and model selection are presented, and the asymptotic properties of these statistics are examined.
Estimation for an additive growth curve model with orthogonal design matrices
Hu, Jianhua; You, Jinhong; 10.3150/10-BEJ315
2012-01-01
An additive growth curve model with orthogonal design matrices is proposed in which observations may have different profile forms. The proposed model allows us to fit data and then estimate parameters in a more parsimonious way than the traditional growth curve model. Two-stage generalized least-squares estimators for the regression coefficients are derived where a quadratic estimator for the covariance of observations is taken as the first-stage estimator. Consistency, asymptotic normality and asymptotic independence of these estimators are investigated. Simulation studies and a numerical example are given to illustrate the efficiency and parsimony of the proposed model for model specifications in the sense of minimizing Akaike's information criterion (AIC).
Estimation in semi-parametric regression with non-stationary regressors
Chen, Jia; Li, Degui; 10.3150/10-BEJ344
2012-01-01
In this paper, we consider a partially linear model of the form $Y_t=X_t^{\\tau}\\theta_0+g(V_t)+\\epsilon_t$, $t=1,...,n$, where $\\{V_t\\}$ is a $\\beta$ null recurrent Markov chain, $\\{X_t\\}$ is a sequence of either strictly stationary or non-stationary regressors and $\\{\\epsilon_t\\}$ is a stationary sequence. We propose to estimate both $\\theta_0$ and $g(\\cdot)$ by a semi-parametric least-squares (SLS) estimation method. Under certain conditions, we then show that the proposed SLS estimator of $\\theta_0$ is still asymptotically normal with the same rate as for the case of stationary time series. In addition, we also establish an asymptotic distribution for the nonparametric estimator of the function $g(\\cdot)$. Some numerical examples are provided to show that our theory and estimation method work well in practice.
Quasi-likelihood estimation of average treatment effects based on model information
Institute of Scientific and Technical Information of China (English)
Zhi-hua SUN
2007-01-01
In this paper, the estimation of average treatment effects is considered when we have the model information of the conditional mean and conditional variance for the responses given the covariates. The quasi-likelihood method adapted to treatment effects data is developed to estimate the parameters in the conditional mean and conditional variance models. Based on the model information, we define three estimators by imputation, regression and inverse probability weighted methods.All the estimators are shown asymptotically normal. Our simulation results show that by using the model information, the substantial efficiency gains are obtained which are comparable with the existing estimators.
Quasi-likelihood estimation of average treatment effects based on model information
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper, the estimation of average treatment effects is considered when we have the model information of the conditional mean and conditional variance for the responses given the covariates. The quasi-likelihood method adapted to treatment effects data is developed to estimate the parameters in the conditional mean and conditional variance models. Based on the model information, we define three estimators by imputation, regression and inverse probability weighted methods. All the estimators are shown asymptotically normal. Our simulation results show that by using the model information, the substantial efficiency gains are obtained which are comparable with the existing estimators.
Estimation of Semi-Varying Coefficient Model with Surrogate Data and Validation Sampling
Institute of Scientific and Technical Information of China (English)
Ya-zhao L(U); Ri-quan ZHANG; Zhen-sheng HUANG
2013-01-01
In this paper,we investigate the estimation of semi-varying coefficient models when the nonlinear covariates are prone to measurement error.With the help of validation sampling,we propose two estimators of the parameter and the coefficient functions by combining dimension reduction and the profile likelihood methods without any error structure equation specification or error distribution assumption.We establish the asymptotic normality of proposed estimators for both the parametric and nonparametric parts and show that the proposed estimators achieves the best convergence rate.Data-driven bandwidth selection methods are also discussed.Simulations are conducted to evaluate the finite sample property of the estimation methods proposed.
DEFF Research Database (Denmark)
Effraimidis, Georgios; Dahl, Christian Møller
In this paper, we develop a fully nonparametric approach for the estimation of the cumulative incidence function with Missing At Random right-censored competing risks data. We obtain results on the pointwise asymptotic normality as well as the uniform convergence rate of the proposed nonparametric...... estimator. A simulation study that serves two purposes is provided. First, it illustrates in details how to implement our proposed nonparametric estimator. Secondly, it facilitates a comparison of the nonparametric estimator to a parametric counterpart based on the estimator of Lu and Liang (2008...
Institute of Scientific and Technical Information of China (English)
XU Shunshan; A. F. NIETO-SAMANIEGO; S. A. ALANIZ-(A)LVAREZ
2005-01-01
The Sierra de San Miguelito is a relatively uplifted area and is constituted by a large amount of silicic volcanic rocks with ages from middle to late Cenozoic. The normal faults of the Sierra de San Miguelito are Domino-style and nearly parallel. The cumulative length and displacement of the faults obey power-law distribution. The fractal dimension of the fault traces is -1.49. Using the multi-line one-dimensional sampling, the calculated exponent of cumulative fault displacements is -0.66. A cumulative curve combining measurements of all four sections yielded a slope of -0.63. The displacement-length plot shows a non-linear relationship and large dispersion of data. The large dispersion in the plot is mainly due to the fault linkage during faulting. An estimation of extensional strain due to the normal faults is ca. 0.1830.The bed extension strain is always less than or equal to the horizontal extension strain. The deformation in the Sierra de San Miguelito occurred near the surface, producing pervasive faults and many faults are too small to appear in maps and sections at common scales. The stretching produced by small faults reach ca. 33% of the total horizontal elongation.
Directory of Open Access Journals (Sweden)
Ömer Kavaklıoğlu
2011-01-01
Full Text Available We have presented a derivation of the asymptotic equations for transverse magnetic multiple scattering coefficients of an infinite grating of penetrable circular cylinders for obliquely incident plane electromagnetic waves. We have first deducted an “Ansatz” delineating the asymptotic behavior of the transverse magnetic multiple scattering coefficients associated with the most generalized condition of oblique incidence (Kavaklıoğlu, 2000 by exploiting Schlömilch series corresponding to the special circumstance that the grating spacing is much smaller than the wavelength of the incident electromagnetic radiation. The validity of the asymptotic equations for the aforementioned scattering coefficients has been verified by collating them with the Twersky's asymptotic equations at normal incidence. Besides, we have deduced the consequences that the asymptotic forms of the equations at oblique incidence acquired in this paper reduce to Twersky's asymptotic forms at normal incidence by expanding the generalized scattering coefficients at oblique incidence into an asymptotic series as a function of the ratio of the cylinder radius to the grating spacing.
The optimal homotopy asymptotic method engineering applications
Marinca, Vasile
2015-01-01
This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011, and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five application...
Lectures on renormalization and asymptotic safety
Nagy, Sandor
2012-01-01
A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety. It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization. We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross-Neveu model, the nonlinear $\\sigma$ model, the sine-Gordon model, and the model of quantum Einstein gravity. We also give a detailed analysis of infrared behavior of the models where a spontaneous symmetry breaking takes place. The deep infrared behavior of the broken phase cannot be treated within the framework of perturbative calculations. We demonstrate that there exists an infrared fixed point in the broken phase which creates a new scaling regime there, however its structure ...
Asymptotic analysis of outwardly propagating spherical flames
Institute of Scientific and Technical Information of China (English)
Yun-Chao Wu; Zheng Chen
2012-01-01
Asymptotic analysis is conducted for outwardly propagating spherical flames with large activation energy.The spherical flame structure consists of the preheat zone,reaction zone,and equilibrium zone.Analytical solutions are separately obtained in these three zones and then asymptotically matched.In the asymptotic analysis,we derive a correlation describing the spherical flame temperature and propagation speed changing with the flame radius.This correlation is compared with previous results derived in the limit of infinite value of activation energy.Based on this correlation,the properties of spherical flame propagation are investigated and the effects of Lewis number on spherical flame propagation speed and extinction stretch rate are assessed.Moreover,the accuracy and performance of different models used in the spherical flame method are examined.It is found that in order to get accurate laminar flame speed and Markstein length,non-linear models should be used.
Relations between asymptotic and Fredholm representations
Manuilov, V M
1997-01-01
We prove that for matrix algebras $M_n$ there exists a monomorphism $(\\prod_n M_n/\\oplus_n M_n)\\otimes C(S^1) \\to {\\cal Q} $ into the Calkin algebra which induces an isomorphism of the $K_1$-groups. As a consequence we show that every vector bundle over a classifying space $B\\pi$ which can be obtained from an asymptotic representation of a discrete group $\\pi$ can be obtained also from a representation of the group $\\pi\\times Z$ into the Calkin algebra. We give also a generalization of the notion of Fredholm representation and show that asymptotic representations can be viewed as asymptotic Fredholm representations.
On generalized Nariai solutions and their asymptotics
Beyer, Florian
2009-01-01
In this paper, we consider the class of generalized Nariai solutions of Einstein's field equations in vacuum with a positive cosmological constant. According to the cosmic no-hair conjecture, generic expanding solutions isotropize and approach the de-Sitter solution asymptotically, at least locally in space. The generalized Nariai solutions, however, show quite unusual asymptotics and hence should be non-generic in some sense. In the first part of the paper, we list the necessary facts and characterize the asymptotic behavior geometrically. In the second part, we study the question of non-genericity, which we are able to confirm within the class of spatially homogeneous solutions. It turns out that perturbations of the three isometry classes of generalized Nariai solutions are related to different mass regimes of Schwarzschild de-Sitter solutions. In subsequent papers, we will continue this research in more general classes of solutions.
Energy Technology Data Exchange (ETDEWEB)
Naderi, S Mehdizadeh [Radiation Research Center, Shiraz university, Shiraz, Fars (Iran, Islamic Republic of); Karimipourfard, M; Lotfalizadeh, F [Radiation medicine department, school of mechanical engineering, Shiraz uni, Shiraz, Fars (Iran, Islamic Republic of); Zamani, E; Molaeimanesh, Z; Sadeghi, M; Sina, S; Faghihi, R [Shiraz University, Shiraz, Fars (Iran, Islamic Republic of); Entezarmahdi, M [Shahid Beheshti University, Shiraz, Fars (Iran, Islamic Republic of)
2015-06-15
Purpose: I-131 is one of the most frequent radionuclides used in nuclear medicine departments. The radiation workers, who manipulate the unsealed radio-toxic iodine, should be monitored for internal contamination. In this study a protocol was established for estimating I-131 activity absorbed in the thyroid glands of the nuclear medicine staff in normal working condition and also in accidents. Methods: I-131 with the activity of 10 μCi was injected inside the thyroid gland of a home-made anthropomorphic neck phantom. The phantom is made up of PMMA as soft tissue, and Aluminium as bone. The dose rate at different distances from the surface of the neck phantom was measured using a scintillator detector for duration of two months. Then, calibration factors were obtained, for converting the dose rate at each distance to the iodine activity inside the thyroid. Results: According to the results of this study, the calibration factors for converting the dose rates (nSv/h) at distances of 0cm, 1cm, 6cm, 11cm, and 16cm to the activity (kBq) inside the thyroid were found to be 0.03, 0.04, 0.14, 0.29, and 0.49 . Conclusion: This method can be effectively used for quick estimation of the I-131 concentration inside the thyroid of the staff for daily checks in normal working conditions and also in accidents.
On an asymptotic distribution of dependent random variables on a 3-dimensional lattice✩
Harvey, Danielle J.; Weng, Qian; Beckett, Laurel A.
2010-01-01
We define conditions under which sums of dependent spatial data will be approximately normally distributed. A theorem on the asymptotic distribution of a sum of dependent random variables defined on a 3-dimensional lattice is presented. Examples are also presented. PMID:20436940
Asymptotics of a horizontal liquid bridge
Haynes, M.; O'Brien, S. B. G.; Benilov, E. S.
2016-04-01
This paper uses asymptotic techniques to find the shape of a two dimensional liquid bridge suspended between two vertical walls. We model the equilibrium bridge shape using the Laplace-Young equation. We use the Bond number as a small parameter to deduce an asymptotic solution which is then compared with numerical solutions. The perturbation approach demonstrates that equilibrium is only possible if the contact angle lies within a hysteresis interval and the analysis relates the width of this interval to the Bond number. This result is verified by comparison with a global force balance. In addition, we examine the quasi-static evolution of such a two dimensional bridge.
Semiclassical Asymptotics on Manifolds with Boundary
Koldan, Nilufer; Shubin, Mikhail
2008-01-01
We discuss semiclassical asymptotics for the eigenvalues of the Witten Laplacian for compact manifolds with boundary in the presence of a general Riemannian metric. To this end, we modify and use the variational method suggested by Kordyukov, Mathai and Shubin (2005), with a more extended use of quadratic forms instead of the operators. We also utilize some important ideas and technical elements from Helffer and Nier (2006), who were the first to supply a complete proof of the full semi-classical asymptotic expansions for the eigenvalues with fixed numbers.
Asymptotic Methods for Solitary Solutions and Compactons
Directory of Open Access Journals (Sweden)
Ji-Huan He
2012-01-01
Full Text Available This paper is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations. Particular attention is paid throughout the paper to giving an intuitive grasp for the variational approach, the Hamiltonian approach, the variational iteration method, the homotopy perturbation method, the parameter-expansion method, the Yang-Laplace transform, the Yang-Fourier transform, and ancient Chinese mathematics. Hamilton principle and variational principles are also emphasized. The reviewed asymptotic methods are easy to be followed for various applications. Some ideas on this paper are first appeared.
Asymptotic stability of singularly perturbed differential equations
Artstein, Zvi
2017-02-01
Asymptotic stability is examined for singularly perturbed ordinary differential equations that may not possess a natural split into fast and slow motions. Rather, the right hand side of the equation is comprised of a singularly perturbed component and a regular one. The limit dynamics consists then of Young measures, with values being invariant measures of the fast contribution, drifted by the slow one. Relations between the asymptotic stability of the perturbed system and the limit dynamics are examined, and a Lyapunov functions criterion, based on averaging, is established.
Equations of States in Singular Statistical Estimation
Watanabe, Sumio
2007-01-01
Learning machines which have hierarchical structures or hidden variables are singular statistical models because they are nonidentifiable and their Fisher information matrices are singular. In singular statistical models, neither the Bayes a posteriori distribution converges to the normal distribution nor the maximum likelihood estimator satisfies asymptotic normality. This is the main reason why it has been difficult to predict their generalization performances from trained states. In this paper, we study four errors, (1) Bayes generalization error, (2) Bayes training error, (3) Gibbs generalization error, and (4) Gibbs training error, and prove that there are mathematical relations among these errors. The formulas proved in this paper are equations of states in statistical estimation because they hold for any true distribution, any parametric model, and any a priori distribution. Also we show that Bayes and Gibbs generalization errors are estimated by Bayes and Gibbs training errors, and propose widely appl...
Directory of Open Access Journals (Sweden)
Paul S. Addison
2015-01-01
Full Text Available DPOP (ΔPOP or Delta-POP is a noninvasive parameter which measures the strength of respiratory modulations present in the pulse oximeter waveform. It has been proposed as a noninvasive alternative to pulse pressure variation (PPV used in the prediction of the response to volume expansion in hypovolemic patients. We considered a number of simple techniques for better determining the underlying relationship between the two parameters. It was shown numerically that baseline-induced signal errors were asymmetric in nature, which corresponded to observation, and we proposed a method which combines a least-median-of-squares estimator with the requirement that the relationship passes through the origin (the LMSO method. We further developed a method of normalization of the parameters through rescaling DPOP using the inverse gradient of the linear fitted relationship. We propose that this normalization method (LMSO-N is applicable to the matching of a wide range of clinical parameters. It is also generally applicable to the self-normalizing of parameters whose behaviour may change slightly due to algorithmic improvements.
Two-step estimation for inhomogeneous spatial point processes
DEFF Research Database (Denmark)
Waagepetersen, Rasmus; Guan, Yongtao
2009-01-01
The paper is concerned with parameter estimation for inhomogeneous spatial point processes with a regression model for the intensity function and tractable second-order properties (K-function). Regression parameters are estimated by using a Poisson likelihood score estimating function and in the ......The paper is concerned with parameter estimation for inhomogeneous spatial point processes with a regression model for the intensity function and tractable second-order properties (K-function). Regression parameters are estimated by using a Poisson likelihood score estimating function...... and in the second step minimum contrast estimation is applied for the residual clustering parameters. Asymptotic normality of parameter estimates is established under certain mixing conditions and we exemplify how the results may be applied in ecological studies of rainforests....
Heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions.
Lachos, Victor H; Bandyopadhyay, Dipankar; Garay, Aldo M
2011-08-01
An extension of some standard likelihood based procedures to heteroscedastic nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. We derive a simple EM-type algorithm for iteratively computing maximum likelihood (ML) estimates and the observed information matrix is derived analytically. Simulation studies demonstrate the robustness of this flexible class against outlying and influential observations, as well as nice asymptotic properties of the proposed EM-type ML estimates. Finally, the methodology is illustrated using an ultrasonic calibration data.
Asymptotic Distributions for Tests of Combined Significance.
Becker, Betsy Jane
This paper discusses distribution theory and power computations for four common "tests of combined significance." These tests are calculated using one-sided sample probabilities or p values from independent studies (or hypothesis tests), and provide an overall significance level for the series of results. Noncentral asymptotic sampling…
Breaking a magnetic zero locus: asymptotic analysis
Raymond, Nicolas
2014-01-01
25 pages; This paper deals with the spectral analysis of the Laplacian in presence of a magnetic field vanishing along a broken line. Denoting by $\\theta$ the breaking angle, we prove complete asymptotic expansions of all the lowest eigenpairs when $\\theta$ goes to $0$. The investigation deeply uses a coherent states decomposition and a microlocal analysis of the eigenfunctions.
Asymptotic iteration approach to supersymmetric bistable potentials
Institute of Scientific and Technical Information of China (English)
H. Ciftci; O. ozer; P. Roy
2012-01-01
We examine quasi exactly solvable bistable potentials and their supersymmetric partners within the framework of the asymptotic iteration method (AIM).It is shown that the AIM produces excellent approximate spectra and that sometimes it is found to be more useful to use the partner potential for computation. We also discuss the direct application of the AIM to the Fokker-Planck equation.
The conformal approach to asymptotic analysis
Nicolas, Jean-Philippe
2015-01-01
This essay was written as an extended version of a talk given at a conference in Strasbourg on "Riemann, Einstein and geometry", organized by Athanase Papadopoulos in September 2014. Its aim is to present Roger Penrose's approach to asymptotic analysis in general relativity, which is based on conformal geometric techniques, focusing on historical and recent aspects of two specialized topics~: conformal scattering and peeling.
Asymptotic symmetry algebra of conformal gravity
Irakleidou, M
2016-01-01
We compute asymptotic symmetry algebras of conformal gravity. Due to more general boundary conditions allowed in conformal gravity in comparison to those in Einstein gravity, we can classify the corresponding algebras. The highest algebra for non-trivial boundary conditions is five dimensional and it leads to global geon solution with non-vanishing charges.
Large degree asymptotics of generalized Bessel polynomials
J.L. López; N.M. Temme (Nico)
2011-01-01
textabstractAsymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given that is valid outside a compact neighborhood of the
THE COMPLETE ASYMPTOTIC EXPANSION FOR BASKAKOV OPERATORS
Institute of Scientific and Technical Information of China (English)
Chungou Zhang; Quane Wang
2007-01-01
In this paper, we derive the complete asymptotic expansion of classical Baskakov itly in terms of Stirling number of the first and second kind and another number G(I, p). As a corollary, we also get the Voronovskaja-type result for the operators.
Fixed Point Theorems for Asymptotically Contractive Multimappings
Directory of Open Access Journals (Sweden)
M. Djedidi
2012-01-01
Full Text Available We present fixed point theorems for a nonexpansive set-valued mapping from a closed convex subset of a reflexive Banach space into itself under some asymptotic contraction assumptions. Some existence results of coincidence points and eigenvalues for multimappings are given.
Couplings and Asymptotic Exponentiality of Exit Times
Brassesco, S.; Olivieri, E.; Vares, M. E.
1998-10-01
The goal of this note is simply to call attention to the resulting simplification in the proof of asymptotic exponentiality of exit times in the Freidlin-Wentzell regime (as proved by F. Martinelli et al.) by using the coupling proposed by T. Lindvall and C. Rogers.
Toeplitz Quantization and Asymptotic Expansions: Geometric Construction
Directory of Open Access Journals (Sweden)
Miroslav Englis
2009-02-01
Full Text Available For a real symmetric domain G_R/K_R, with complexification G_C/K_C, we introduce the concept of ''star-restriction'' (a real analogue of the ''star-products'' for quantization of Kähler manifolds and give a geometric construction of the G_R-invariant differential operators yielding its asymptotic expansion.
On iterative procedures of asymptotic inference
K.O. Dzhaparidze (Kacha)
1983-01-01
textabstractAbstract An informal discussion is given on performing an unconstrained maximization or solving non‐linear equations of statistics by iterative methods with the quadratic termination property. It is shown that if a miximized function, e.g. likelihood, is asymptotically quadratic, then f
Asymptotically periodic solutions of Volterra integral equations
Directory of Open Access Journals (Sweden)
Muhammad N. Islam
2016-03-01
Full Text Available We study the existence of asymptotically periodic solutions of a nonlinear Volterra integral equation. In the process, we obtain the existence of periodic solutions of an associated nonlinear integral equation with infinite delay. Schauder's fixed point theorem is used in the analysis.
On an asymptotically linear elliptic Dirichlet problem
Directory of Open Access Journals (Sweden)
Zhitao Zhang
2002-01-01
Full Text Available Under very simple conditions, we prove the existence of one positive and one negative solution of an asymptotically linear elliptic boundary value problem. Even for the resonant case at infinity, we do not need to assume any more conditions to ensure the boundness of the (PS sequence of the corresponding functional. Moreover, the proof is very simple.
Discrete Energy Asymptotics on a Riemannian circle
Brauchart, J S; Saff, E B
2009-01-01
We derive the complete asymptotic expansion in terms of powers of $N$ for the geodesic $f$-energy of $N$ equally spaced points on a rectifiable simple closed curve $\\Gamma$ in ${\\mathbb R}^p$, $p\\geq2$, as $N \\to \\infty$. For $f$ decreasing and convex, such a point configuration minimizes the $f$-energy $\\sum_{j\
Asymptotic inversion of the Erlang B formula
J. van Leeuwaarden; N.M. Temme (Nico)
2009-01-01
textabstractThe Erlang B formula represents the steady-state blocking probability in the Erlang loss model or $M/M/s/s$ queue. We derive asymptotic expansions for the offered load that matches, for a given number of servers, a certain blocking probability. In addressing this inversion problem we mak
Resonance asymptotics in the generalized Winter model
Exner, P; Exner, Pavel; Fraas, Martin
2006-01-01
We consider a modification of the Winter model describing a quantum particle in presence of a spherical barrier given by a fixed generalized point interaction. It is shown that the three classes of such interactions correspond to three different types of asymptotic behaviour of resonances of the model at high energies.
Gao, Yongnian; Gao, Junfeng; Wang, Jing; Wang, Shuangshuang; Li, Qin; Zhai, Shuhua; Zhou, Ya
2017-12-01
Satellite remote sensing is advantageous for the mapping and monitoring of aquatic vegetation biomass at large spatial scales. We proposed a scale transformation (CT) method of converting the field sampling-site biomass from the quadrat to pixel scale and a new normalized water-adjusted vegetation index (NWAVI) based on remotely sensed imagery for the biomass estimation of aquatic vegetation (excluding emergent vegetation). We used a modeling approach based on the proposed CT method and NWAVI as well as statistical analyses including linear, quadratic, logarithmic, cubic, exponential, inverse and power regression to estimate the aquatic vegetation biomass, and we evaluated the performance of the biomass estimation. We mapped the spatial distribution and temporal change of the aquatic vegetation biomass using a geographic information system in a test lake in different months. The exponential regression models based on CT and the NWAVI had optimal adjusted R(2), F and Sig. values in both May and August 2013. The scatter plots of the observed versus the predicted biomass showed that most of the validated field sites were near the 1:1 line. The RMSE, ARE and RE values were small. The spatial distribution and change of the aquatic vegetation biomass in the study area showed clear variability. Among the NWAVI-based and other vegetation index-based models, the CT and NWAVI-based models had the largest adjusted R(2), F and the smallest ARE values in both tests. The proposed modeling scheme is effective for the biomass estimation of aquatic vegetation in lakes. It indicated that the proposed method can provide a most accurate spatial distribution map of aquatic vegetation biomass for lake ecological management. More accurate biomass maps of aquatic vegetation are essential for implementing conservation policy and for reducing uncertainties in our understanding of the lake carbon cycle. Copyright © 2017 Elsevier B.V. All rights reserved.
Stokes Waves Revisited: Exact Solutions in the Asymptotic Limit
Davies, Megan
2016-01-01
Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic secular variation in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long standing theoretical insufficiency by invoking a compact exact $n$-ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third ordered perturbative solution, that leads to a seamless extension to higher order (e.g. fifth order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desir...
Asymptotic Behavior of the Newton-Boussinesq Equation in a Two-Dimensional Channel
Fucci, Guglielmo; Singh, Preeti
2007-01-01
We prove the existence of a global attractor for the Newton-Boussinesq equation defined in a two-dimensional channel. The asymptotic compactness of the equation is derived by the uniform estimates on the tails of solutions. We also establish the regularity of the global attractor.
IDENTIFICATION ERROR BOUNDS AND ASYMPTOTIC DISTRIBUTIONS FOR SYSTEMS WITH STRUCTURAL UNCERTAINTIES
Institute of Scientific and Technical Information of China (English)
Gang George YIN; Shaobai KAN; Le Yi WANG
2006-01-01
This work is concerned with identification of systems that are subject to not only measurement noises, but also structural uncertainties such as unmodeled dynamics, sensor nonlinear mismatch,and observation bias. Identification errors are analyzed for their dependence on these structural uncertainties. Asymptotic distributions of scaled sequences of estimation errors are derived.
The asymptotic D-state to S-state ratio of triton
Indian Academy of Sciences (India)
Hossen Sadeghi; Reza Pourimani; Hassan Khalili
2013-11-01
At low energies, an effective field theory (EFT) with only contact interactions as well as three-body forces allow a detailed analysis of renormalization in a non-perturbative context and uncovers novel asymptotic behaviour. Triton as a three-body system, based on the EFT have been previously shown to provide representative binding energies, charge radii, S-wave scattering amplitude and asymptotic normalization constants for the 3H bound state system. Herein, EFT predictions of the asymptotic D-state to S-state ratio of triton are calculated to more fully evaluate the adequacy of the EFT model. Manifestly model-independent calculations can be carried out to high orders, leading to high precision.
The renormalization method based on the Taylor expansion and applications for asymptotic analysis
Liu, Cheng-shi
2016-01-01
Based on the Taylor expansion, we propose a renormalization method for asymptotic analysis. The standard renormalization group (RG) method for asymptotic analysis can be derived out from this new method, and hence the mathematical essence of the RG method is also recovered. The biggest advantage of the proposed method is that the secular terms in perturbation series are automatically eliminated, but in usual perturbation theory, we need more efforts and tricks to eliminate these terms. At the same time, the mathematical foundation of the method is simple and the logic of the method is very clear, therefore, it is very easy in practice. As application, we obtain the uniform valid asymptotic solutions to some problems including vector field, boundary layer and boundary value problems of nonlinear wave equations. Moreover, we discuss the normal form theory and reduction equations of dynamical systems. Furthermore, by combining the topological deformation and the RG method, a modified method namely the homotopy r...
Duggin, M. J. (Principal Investigator); Piwinski, D.
1982-01-01
The use of NOAA AVHRR data to map and monitor vegetation types and conditions in near real-time can be enhanced by using a portion of each GAC image that is larger than the central 25% now considered. Enlargement of the cloud free image data set can permit development of a series of algorithms for correcting imagery for ground reflectance and for atmospheric scattering anisotropy within certain accuracy limits. Empirical correction algorithms used to normalize digital radiance or VIN data must contain factors for growth stage and for instrument spectral response. While it is not possible to correct for random fluctuations in target radiance, it is possible to estimate the necessary radiance difference between targets in order to provide target discrimination and quantification within predetermined limits of accuracy. A major difficulty lies in the lack of documentation of preprocessing algorithms used on AVHRR digital data.
DEFF Research Database (Denmark)
Gaihede, Michael Lyhne; Donghua, Liao; Gregersen, H.
2007-01-01
are related to these, but studies are few and mostly not comparable. The elastic properties of membranes can be described by the areal modulus, and these may also be susceptible to age-related changes reflected by changes in the areal modulus. The areal modulus is determined by the relationship between...... a younger (n = 10) and an older (n = 10) group of normal subjects. The areal modulus for lateral and medial displacement of the tympanic membrane system was smaller in the older group (mean = 0.686 and 0.828 kN m(-1), respectively) compared to the younger group (mean = 1.066 and 1.206 kN m(-1), respectively...... finite element analyses. In vivo estimates of Young's modulus in this study were a factor 2-3 smaller than previously found in vitro. No significant age-related differences were found in the elastic properties as expressed by the areal modulus....
Ultraviolet asymptotics for quasiperiodic AdS_4 perturbations
Craps, Ben; Jai-akson, Puttarak; Vanhoof, Joris
2015-01-01
Spherically symmetric perturbations in AdS-scalar field systems of small amplitude epsilon approximately periodic on time scales of order 1/epsilon^2 (in the sense that no significant transfer of energy between the AdS normal modes occurs) have played an important role in considerations of AdS stability. They are seen as anchors of stability islands where collapse of small perturbations to black holes does not occur. (This collapse, if it happens, typically develops on time scales of the order 1/epsilon^2.) We construct an analytic treatment of the frequency spectra of such quasiperiodic perturbations, paying special attention to the large frequency asymptotics. For the case of a self-interacting phi^4 scalar field in a non-dynamical AdS background, we arrive at a fairly complete analytic picture involving quasiperiodic spectra with an exponential suppression modulated by a power law at large mode numbers. For the case of dynamical gravity, the structure of the large frequency asymptotics is more complicated....
Ultraviolet asymptotics for quasiperiodic AdS{sub 4} perturbations
Energy Technology Data Exchange (ETDEWEB)
Craps, Ben [Theoretische Natuurkunde, Vrije Universiteit Brussel and The International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium); Evnin, Oleg [Department of Physics, Faculty of Science, Chulalongkorn University,Thanon Phayathai, Pathumwan, Bangkok 10330 (Thailand); Theoretische Natuurkunde, Vrije Universiteit Brussel and The International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium); Jai-akson, Puttarak [Department of Physics, Faculty of Science, Chulalongkorn University,Thanon Phayathai, Pathumwan, Bangkok 10330 (Thailand); Vanhoof, Joris [Theoretische Natuurkunde, Vrije Universiteit Brussel and The International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium)
2015-10-12
Spherically symmetric perturbations in AdS-scalar field systems of small amplitude ε approximately periodic on time scales of order 1/ε{sup 2} (in the sense that no significant transfer of energy between the AdS normal modes occurs) have played an important role in considerations of AdS stability. They are seen as anchors of stability islands where collapse of small perturbations to black holes does not occur. (This collapse, if it happens, typically develops on time scales of the order 1/ε{sup 2}.) We construct an analytic treatment of the frequency spectra of such quasiperiodic perturbations, paying special attention to the large frequency asymptotics. For the case of a self-interacting ϕ{sup 4} scalar field in a non-dynamical AdS background, we arrive at a fairly complete analytic picture involving quasiperiodic spectra with an exponential suppression modulated by a power law at large mode numbers. For the case of dynamical gravity, the structure of the large frequency asymptotics is more complicated. We give analytic explanations for the general qualitative features of quasiperiodic solutions localized around a single mode, in close parallel to our discussion of the probe scalar field, and find numerical evidence for logarithmic modulations in the gravitational quasiperiodic spectra existing on top of the formulas previously reported in the literature.
Wave attractors and the asymptotic dissipation rate of tidal disturbances
Ogilvie, G I
2005-01-01
Linear waves in bounded inviscid fluids do not generally form normal modes with regular eigenfunctions. Examples are provided by inertial waves in a rotating fluid contained in a spherical annulus, and internal gravity waves in a stratified fluid contained in a tank with a non-rectangular cross-section. For wave frequencies in the ranges of interest, the inviscid linearized equations are spatially hyperbolic and their characteristic rays are typically focused on to wave attractors. When these systems experience periodic forcing, for example of tidal origin, the response of the fluid can become localized in the neighbourhood of a wave attractor. In this paper I define a prototypical problem of this form and construct analytically the long-term response to a periodic body force in the asymptotic limit of small viscosity. The vorticity of the fluid is localized in a detached shear layer close to the wave attractor in such a way that the total rate of dissipation of energy is asymptotically independent of the vis...
Asymptotic expansion of the wavelet transform with error term
Pathak, R.S.; Pathak, Ashish
2014-01-01
UsingWong's technique asymptotic expansion for the wavelet transform is derived and thereby asymptotic expansions for Morlet wavelet transform, Mexican Hat wavelet transform and Haar wavelet transform are obtained.
Asymptotic modelling of a thermopiezoelastic anisotropic smart plate
Long, Yufei
Motivated by the requirement of modelling for space flexible reflectors as well as other applications of plate structures in engineering, a general anisotropic laminated thin plate model and a monoclinic Reissner-Mindlin plate model with thermal deformation, two-way coupled piezoelectric effect and pyroelectric effect is constructed using the variational asymptotic method, without any ad hoc assumptions. Total potential energy contains strain energy, electric potential energy and energy caused by temperature change. Three-dimensional strain field is built based on the concept of warping function and decomposition of the rotation tensor. The feature of small thickness and large in-plane dimension of plate structure helped to asymptotically simplify the three-dimensional analysis to a two-dimensional analysis on the reference surface and a one-dimensional analysis through the thickness. For the zeroth-order approximation, the asymptotically correct expression of energy is derived into the form of energetic equation in classical laminated plate theory, which will be enough to predict the behavior of plate structures as thin as a space flexible reflector. A through-the-thickness strain field can be expressed in terms of material constants and two-dimensional membrane and bending strains, while the transverse normal and shear stresses are not predictable yet. In the first-order approximation, the warping functions are further disturbed into a high order and an asymptotically correct energy expression with derivatives of the two-dimensional strains is acquired. For the convenience of practical use, the expression is transformed into a Reissner-Mindlin form with optimization implemented to minimize the error. Transverse stresses and strains are recovered using the in-plane strain variables. Several numerical examples of different laminations and shapes are studied with the help of analytical solutions or shell elements in finite element codes. The constitutive relation is
Efficient estimation of semiparametric copula models for bivariate survival data
Cheng, Guang
2014-01-01
A semiparametric copula model for bivariate survival data is characterized by a parametric copula model of dependence and nonparametric models of two marginal survival functions. Efficient estimation for the semiparametric copula model has been recently studied for the complete data case. When the survival data are censored, semiparametric efficient estimation has only been considered for some specific copula models such as the Gaussian copulas. In this paper, we obtain the semiparametric efficiency bound and efficient estimation for general semiparametric copula models for possibly censored data. We construct an approximate maximum likelihood estimator by approximating the log baseline hazard functions with spline functions. We show that our estimates of the copula dependence parameter and the survival functions are asymptotically normal and efficient. Simple consistent covariance estimators are also provided. Numerical results are used to illustrate the finite sample performance of the proposed estimators. © 2013 Elsevier Inc.
Generalized Jackknife Estimators of Weighted Average Derivatives
DEFF Research Database (Denmark)
Cattaneo, Matias D.; Crump, Richard K.; Jansson, Michael
With the aim of improving the quality of asymptotic distributional approximations for nonlinear functionals of nonparametric estimators, this paper revisits the large-sample properties of an important member of that class, namely a kernel-based weighted average derivative estimator. Asymptotic li...
Maximum likelihood estimation of fractionally cointegrated systems
DEFF Research Database (Denmark)
Lasak, Katarzyna
to the equilibrium parameters and the variance-covariance matrix of the error term. We show that using ML principles to estimate jointly all parameters of the fractionally cointegrated system we obtain consistent estimates and provide their asymptotic distributions. The cointegration matrix is asymptotically mixed...
Non-asymptotic fractional order differentiators via an algebraic parametric method
Liu, Dayan
2012-08-01
Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie\\'s modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.
Dybalski, Wojciech; Møller, Jacob Schach
2015-11-01
We show asymptotic completeness of two-body scattering for a class of translation invariant models describing a single quantum particle (the electron) linearly coupled to a massive scalar field (bosons). Our proof is based on a recently established Mourre estimate for these models. In contrast to previous approaches, it requires no number cutoff, no restriction on the particle-field coupling strength, and no restriction on the magnitude of total momentum. Energy, however, is restricted by the two-boson threshold, admitting only scattering of a dressed electron and a single asymptotic boson. The class of models we consider include the UV-cutoff Nelson and polaron models.
Moments of q-Normal and conditional q-Normal distributions
2015-01-01
We calculate moments and moment generating functions of two distributions: the so called $q-$Normal and the so called conditional $q-$Normal distributions. These distributions generalize both Normal ($q=1),$ Wigner ($% q=0,$ $q-$Normal) and Kesten-McKay ($q=0,$ conditional $q-$Normal) distributions. As a by product we get asymptotic properties of some expansions in modified Bessel functions.
Variable bandwidth and one-step local M-estimator
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A robust version of local linear regression smoothers augmented with variable bandwidth is studied. The proposed method inherits the advantages of local polynomial regression and overcomes the shortcoming of lack of robustness of least-squares techniques. The use of variable bandwidth enhances the flexibility of the resulting local M-estimators and makes them possible to cope well with spatially inhomogeneous curves, heteroscedastic errors and nonuniform design densities. Under appropriate regularity conditions, it is shown that the proposed estimators exist and are asymptotically normal. Based on the robust estimation equation, one-step local M-estimators are introduced to reduce computational burden. It is demonstrated that the one-step local M-estimators share the same asymptotic distributions as the fully iterative M-estimators, as long as the initial estimators are good enough. In other words, the one-step local M-estimators reduce significantly the computation cost of the fully iterative M-estimators without deteriorating their performance. This fact is also illustrated via simulations.
Locally Asymptotic-norming Property and Kadec Property
Institute of Scientific and Technical Information of China (English)
王建华
2002-01-01
In this paper we study the three new asymptotic-norming properties which are called locally asymptotic-norming property κ, κ=Ⅰ,Ⅱ,Ⅲ,and discuss the relationship between the locally asymptotic-norming property and the Kadec Property.
Preheating in an asymptotically safe quantum field theory
DEFF Research Database (Denmark)
Svendsen, Ole; Moghaddam, Hossein Bazrafshan; Brandenberger, Robert
2016-01-01
We consider reheating in a class of asymptotically safe quantum field theories recently studied in [D. F. Litim and F. Sannino, Asymptotic safety guaranteed, J. High Energy Phys. 12 (2014) 178; D. F. Litim, M. Mojaza, and F. Sannino, Vacuum stability of asymptotically safe gauge-Yukawa theories, ...
Siqueira, J B; Oba, E; Pinho, R O; Quintino, H P; Eler, J P; Miranda Neto, T; Guimarães, S E F; Guimarães, J D
2012-04-01
The present work aimed to estimate heritability and genetic correlations of reproductive features of Nellore bulls, offspring of mothers classified as superprecocious (M1), precocious (M2) and normal (M3). Twenty one thousand hundred and eighty-six animals with average age of 21.29 months were used, evaluated through the breeding soundness evaluation from 1999 to 2008. The breeding soundness features included physical semen evaluation (progressive sperm motility and sperm vigour), semen morphology (major, minor and total sperm defects), scrotal circumference (SC), testicular volume (TV) and SC at 18 months of age (SC18). The components of variance, heritability and genetic correlations for and between the features were estimated simultaneously by restricted maximum likelihood, with the use of the vce software system vs 6. The heritability estimates were high for SC18, SC and TV (0.43, 0.63 and 0.54; 0.45, 0.45 and 0.44; 0.42, 0.45 and 0.41, respectively for the categories of mothers M1, M2 and M3) and low for physical and morphological semen aspects. The genetic correlations between SC18 and SC were high, as well as between these variables with TV. High and positive genetic correlations were recorded among SC18, SC and TV with the physical aspects of the semen, although no favourable association was verified with the morphological aspects, for the three categories of mothers. It can be concluded that the mother's sexual precocity did not affect the heritability of their offspring reproduction features.
Asymptotic Delay Analysis for Cross-Layer Delay-Based Routing in Ad Hoc Networks
Directory of Open Access Journals (Sweden)
Philippe Jacquet
2007-01-01
Full Text Available This paper addresses the problem of the evaluation of the delay distribution via analytical means in IEEE 802.11 wireless ad hoc networks. We show that the asymptotic delay distribution can be expressed as a power law. Based on the latter result, we present a cross-layer delay estimation protocol and we derive new delay-distribution-based routing algorithms, which are well adapted to the QoS requirements of real-time multimedia applications. In fact, multimedia services are not sensitive to average delays, but rather to the asymptotic delay distributions. Indeed, video streaming applications drop frames when they are received beyond a delay threshold, determined by the buffer size. Although delay-distribution-based routing is an NP-hard problem, we show that it can be solved in polynomial time when the delay threshold is large, because of the asymptotic power law distribution of the link delays.
Koopmeiners, Joseph S; 10.1214/11-AOS937
2012-01-01
The receiver operating characteristic (ROC) curve, the positive predictive value (PPV) curve and the negative predictive value (NPV) curve are three measures of performance for a continuous diagnostic biomarker. The ROC, PPV and NPV curves are often estimated empirically to avoid assumptions about the distributional form of the biomarkers. Recently, there has been a push to incorporate group sequential methods into the design of diagnostic biomarker studies. A thorough understanding of the asymptotic properties of the sequential empirical ROC, PPV and NPV curves will provide more flexibility when designing group sequential diagnostic biomarker studies. In this paper, we derive asymptotic theory for the sequential empirical ROC, PPV and NPV curves under case-control sampling using sequential empirical process theory. We show that the sequential empirical ROC, PPV and NPV curves converge to the sum of independent Kiefer processes and show how these results can be used to derive asymptotic results for summaries ...
Asymptotically optimal production policies in dynamic stochastic jobshops with limited buffers
Hou, Yumei; Sethi, Suresh P.; Zhang, Hanqin; Zhang, Qing
2006-05-01
We consider a production planning problem for a jobshop with unreliable machines producing a number of products. There are upper and lower bounds on intermediate parts and an upper bound on finished parts. The machine capacities are modelled as finite state Markov chains. The objective is to choose the rate of production so as to minimize the total discounted cost of inventory and production. Finding an optimal control policy for this problem is difficult. Instead, we derive an asymptotic approximation by letting the rates of change of the machine states approach infinity. The asymptotic analysis leads to a limiting problem in which the stochastic machine capacities are replaced by their equilibrium mean capacities. The value function for the original problem is shown to converge to the value function of the limiting problem. The convergence rate of the value function together with the error estimate for the constructed asymptotic optimal production policies are established.
Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces
Vasy, Andras
2010-01-01
In this paper we develop a general, systematic, microlocal framework for the Fredholm analysis of non-elliptic problems, including high energy (or semiclassical) estimates, which is stable under perturbations. This framework is relatively simple given modern microlocal analysis, and only takes a bit over a dozen pages after the statement of notation. It resides on a compact manifold without boundary, hence in the standard setting of microlocal analysis, including semiclassical analysis. The rest of the paper is devoted to applications. Many natural applications arise in the setting of non-Riemannian b-metrics in the context of Melrose's b-structures. These include asymptotically Minkowski metrics, asymptotically de Sitter-type metrics on a blow-up of the natural compactification and Kerr-de Sitter-type metrics. The simplest application, however, is to provide a new approach to analysis on Riemannian or Lorentzian (or indeed, possibly of other signature) conformally compact spaces (such as asymptotically hyper...
Bridging asymptotic independence and dependence in spatial exbtremes using Gaussian scale mixtures
Huser, Raphaël
2017-06-23
Gaussian scale mixtures are constructed as Gaussian processes with a random variance. They have non-Gaussian marginals and can exhibit asymptotic dependence unlike Gaussian processes, which are asymptotically independent except in the case of perfect dependence. In this paper, we study the extremal dependence properties of Gaussian scale mixtures and we unify and extend general results on their joint tail decay rates in both asymptotic dependence and independence cases. Motivated by the analysis of spatial extremes, we propose flexible yet parsimonious parametric copula models that smoothly interpolate from asymptotic dependence to independence and include the Gaussian dependence as a special case. We show how these new models can be fitted to high threshold exceedances using a censored likelihood approach, and we demonstrate that they provide valuable information about tail characteristics. In particular, by borrowing strength across locations, our parametric model-based approach can also be used to provide evidence for or against either asymptotic dependence class, hence complementing information given at an exploratory stage by the widely used nonparametric or parametric estimates of the χ and χ̄ coefficients. We demonstrate the capacity of our methodology by adequately capturing the extremal properties of wind speed data collected in the Pacific Northwest, US.
Gontscharuk, Veronika; Landwehr, Sandra; Finner, Helmut
2015-01-01
The higher criticism (HC) statistic, which can be seen as a normalized version of the famous Kolmogorov-Smirnov statistic, has a long history, dating back to the mid seventies. Originally, HC statistics were used in connection with goodness of fit (GOF) tests but they recently gained some attention in the context of testing the global null hypothesis in high dimensional data. The continuing interest for HC seems to be inspired by a series of nice asymptotic properties related to this statistic. For example, unlike Kolmogorov-Smirnov tests, GOF tests based on the HC statistic are known to be asymptotically sensitive in the moderate tails, hence it is favorably applied for detecting the presence of signals in sparse mixture models. However, some questions around the asymptotic behavior of the HC statistic are still open. We focus on two of them, namely, why a specific intermediate range is crucial for GOF tests based on the HC statistic and why the convergence of the HC distribution to the limiting one is extremely slow. Moreover, the inconsistency in the asymptotic and finite behavior of the HC statistic prompts us to provide a new HC test that has better finite properties than the original HC test while showing the same asymptotics. This test is motivated by the asymptotic behavior of the so-called local levels related to the original HC test. By means of numerical calculations and simulations we show that the new HC test is typically more powerful than the original HC test in normal mixture models.
The Nonparametric Estimate of Exponential Premium Under Collective Risk Models%聚合风险模型下指数保费的非参数估计
Institute of Scientific and Technical Information of China (English)
张林娜; 温利民; 方婧
2016-01-01
The exponential premium principle is one of the most important premium principles and is wide ‐ly applied in non‐life insurance actuarial science .In this paper ,the nonparametric estimate of exponential premium is investigated under collective risk models .In addition ,the estimator is proved strongly consist‐ent and asymptotically normal .Finally ,a numerical simulation method is used to verify the estimated speed of convergence ,and the asymptotic normality of the estimator is checked in the simulations .%在聚合风险模型的假设下，研究了聚合风险下指数保费的非参数估计，证明了估计的强相合性和渐近正态性。最后通过数值模拟的方法验证了估计的收敛速度及渐近正态性。
Black holes and asymptotically safe gravity
Falls, Kevin; Raghuraman, Aarti
2010-01-01
Quantum gravitational corrections to black holes are studied in four and higher dimensions using a renormalisation group improvement of the metric. The quantum effects are worked out in detail for asymptotically safe gravity, where the short distance physics is characterized by a non-trivial fixed point of the gravitational coupling. We find that a weakening of gravity implies a decrease of the event horizon, and the existence of a Planck-size black hole remnant with vanishing temperature and vanishing heat capacity. The absence of curvature singularities is generic and discussed together with the conformal structure and the Penrose diagram of asymptotically safe black holes. The production cross section of mini-black holes in energetic particle collisions, such as those at the Large Hadron Collider, is analysed within low-scale quantum gravity models. Quantum gravity corrections imply that cross sections display a threshold, are suppressed in the Planckian, and reproduce the semi-classical result in the deep...