2SUR回归模型系数估计的均方误差比较

对于2SUR回归模型的参数估计问题,给出了一些一航均方误差矩阵比较结果,据此提出了一类线性估计和一类基于离差阵广义非限定估计的非线性两步估计,并获得了该两步估计类的一些有限样本性质。     

IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS

In this article, the problem of estimating the covariance matrix in general linear mixed models is considered. Two new classes of estimators obtained by shrinking the eigenvalues towards the origin and the arithmetic mean, respectively, are proposed. It is shown that these new estimators dominate the unbiased estimator under the squared error loss function. Finally, some simulation results to compare the performance of the proposed estimators with that of the unbiased estimator are reported. The simulation results indicate that these new shrinkage estimators provide a substantial improvement in risk under most situations.     

Maximum likelihood estimation of covariance matrices under simple tree ordering

The closed-form maximum likelihood estimators for the completely balanced multivariate one-way random effect model are obtained by Anderson et al. (Ann. Statist. 14 (1986) 405). It remains open whether there exist the closed-form maximum likelihood estimators for the more general completely balanced multivariate multi-way random effects models. In this paper, a new parameterization technique for covariance matrices is used to grasp the inside structure of likelihood function so that the maximum likelihood equations can be dramatically simplified. As such we obtain the closed-form maximum likelihood estimators of covariance matrices for Wishart density functions over the simple tree ordering set, which can then be applied to get the maximum likelihood estimators for the completely balanced multivariate multi-way random effects models without interactions.     

GENERAL MINIMAX ESTIMATORS ON THE LOCATION MATRIX OF A MIXTURE OF NORMALS

This paper considers the estimate problem on the mean matrix of mixtureof normals. In order to evaluate estimators of the mean matrix, a fundamental frameof Ф-(general) decision problem is established. Under the frame, a class of Ф-minimax estimators are constructed.     

多元线性模型中回归系数的线性可容许估计

基于Zellner的平衡损失的思想,本文提出了矩阵形式的平衡损失函数,并在该损失函数下讨论了多元回归系数线性估计的可容许性.给出了六种不同形式的可容许定义,证明了这六种容许性在齐次和非齐次线性估计类中是一致的,且得到了其共同的可容许估计的充要条件.     

Estimation of the Scale Matrix and its Eigenvalues in the Wishart and the Multivariate F Distributions

In this paper, the problem of estimating the scale matrix and their eigenvalues in a Wishart distribution and in a multivariate F distribution (which arise naturally from a two-sample setting) are considered. A new class of estimators which shrink the eigenvalues towards their arithmetic mean are proposed. It is shown that the new estimator which dominates the usual unbiased estimator under the squared error loss function. A simulation study was carried out to study the performance of these estimators.     

Other Classes of Minimax Estimators of Variance Covariance Matrix in Multivariate Normal Distribution

It is well known that the best equivariant estimator of the variance covariance matrix of the multivariate normal distribution with respect to the full affine group of transformation is not even minimax. Some minimax estimators have been proposed. Here we treat this problem in the framework of a multivariate analysis of variance (MANOVA) model and give other classes of minimax estimators.     

The superiority of empirical bayes estimation of parameters in partitioned normal linear model

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.     

Error Process Indexed by Bandwidth Matrices in Multivariate Local Linear Smoothing

We focus on nonparametric multivariate regression function estimation by locally weighted least squares. The asymptotic behavior for a sequence of error processes indexed by bandwidth matrices is derived. We discuss feasible data-driven consistent estimators minimizing asymptotic mean squared error or efficient estimators reducing asymptotic bias at points where opposite sign curvatures of the regression function are present in different directions.     

Optimality of singular vector perturbation under maximum norm

Fan, Wang, and Zhong estimate the difference between the singular vectors of a matrix and those of a perturbed matrix in terms of the maximum norm. Their estimations are used effectively to establish the asymptotic properties of robust covariance estimators (see Journal of Machine Learning Research, 2018;18:1-42). In this paper, we give the corresponding lower bound estimates, which show Fan-Wang-Zhong's estimations optimal.     

矩阵损失函数下回归系数矩阵的非齐次线性估计的可容许性

在二次矩阵损失函数下研究了协方差矩阵未知的多元线性模型中回归系数矩阵的可估线性函数的矩阵非齐次线性估计的可容许性,给出了矩阵非齐次线性估计在线性估计类中可容许的一个充要条件.     

方差分量线性模型中回归系数和参数的所有可容许线性估计

对固定效应方差分量模型，在矩阵损失（ｄ－Ｓ＿τ）（ｄ－Ｓ＿τ）＇下，我们给出了线性可估函数Ｓτ的线性估计在一切估计类中可容许的充要条件；对具有两个方差分量的随机效应线性模型在矩阵损失（ｄ－Ｓα－Ｑβ）（ｄ－Ｓα－Ｑβ）＇下，我们给出了线性可估函数Ｓα＋Ｑβ的线性估计在一切估计类中可容许的充要条件。     

Existence of the uniformly minimum risk equivariant estimators of parameters in a class of normal linear models

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 matrixV and (trV)^α, where α > 0 is 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 ofV 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.     

Bivariate Birnbaum–Saunders distribution and associated inference

Univariate Birnbaum–Saunders distribution has been used quite effectively to model positively skewed data, especially lifetime data and crack growth data. In this paper, we introduce bivariate Birnbaum–Saunders distribution which is an absolutely continuous distribution whose marginals are univariate Birnbaum–Saunders distributions. Different properties of this bivariate Birnbaum–Saunders distribution are then discussed. This new family has five unknown parameters and it is shown that the maximum likelihood estimators can be obtained by solving two non-linear equations. We also propose simple modified moment estimators for the unknown parameters which are explicit and can therefore be used effectively as an initial guess for the computation of the maximum likelihood estimators. We then present the asymptotic distributions of the maximum likelihood estimators and use them to construct confidence intervals for the parameters. We also discuss likelihood ratio tests for some hypotheses of interest. Monte Carlo simulations are then carried out to examine the performance of the proposed estimators. Finally, a numerical data analysis is performed in order to illustrate all the methods of inference discussed here.     

增长曲线模型中UMRE估计和UMRU估计的存在性

对于一般的增长曲线模型,在一般的矩阵损失和二次损失下,用统一的方法分别给出了回归系数矩阵的任一指定可估函数存在一致最小风险同变（ＵＭＲＥ）估计（分别在仿真变换群和转换变换群下）和一致最小风险无编（ＵＭＲＵ）估计的充要条件,以及所有可估函数恒存在ＵＭＲＥ估计和ＵＭＲＵ估计的允要条件。最后将结果应用于一些特殊模型。     

Measurement Error Models with Nonconstant Covariance Matrices

In this paper we consider measurement error models when the observed random vectors are independent and have mean vector and covariance matrix changing with each observation. The asymptotic behavior of the sample mean vector and the sample covariance matrix are studied for such models. Using the derived results, we study the case of the elliptical multiplicative error-in-variables models, providing formal justification for the asymptotic distribution of consistent slope parameter estimators. The model considered extends a normal model previously considered in the literature. Asymptotic relative efficiencies comparing several estimators are also reported.     

二元广义Weibull模型(英文)

本文研究了一个二元广义Weibull分布模型,其边缘分布分别是一元广义Weibull分布.利用EM算法,得到了未知参数的极大似然估计和观测Fisher信息矩阵.     

具有特殊协方差结构的 SURE 模型中参数估计的若干结果

本文讨论具有特殊协方差结构似乎不相关回归方程（SURE）模型中参数的估计问题．除非另有说明,损失函数将取为二次损失和矩阵损失．本文证明了回归系数的线性可估函数的最小二乘估计是极小极大的且在矩阵损失函数下是可容许的;还分别在仿射交换群和平移群下导出了存在回归系数的线性可估函数的一致最小风险同变（UMRE）估计的充要条件,并证明了在仿射交换和二次损失下不存在协方差阵和方差的UMRE估计．     

ASP fits to multi-way layouts

The balanced complete multi-way layout with ordinal or nominal factors is a fundamental data-type that arises in medical imaging, agricultural field trials, DNA microassays, and other settings where analysis of variance (ANOVA) is an established tool. ASP algorithms weigh competing biased fits in order to reduce risk through variance-bias tradeoff. The acronym ASP stands for Adaptive Shrinkage of Penalty bases. Motivating ASP is a penalized least squares criterion that associates a separate quadratic penalty term with each main effect and each interaction in the general ANOVA decomposition of means. The penalty terms express plausible conjecture about the mean function, respecting the difference between ordinal and nominal factors. Multiparametric asymptotics under a probability model and experiments on data elucidate how ASP dominates least squares, sometimes very substantially. ASP estimators for nominal factors recover Stein's superior shrinkage estimators for one- and two-way layouts. ASP estimators for ordinal factors bring out the merits of smoothed fits to multi-way layouts, a topic broached algorithmically in work by Tukey. This research was supported in part by National Science Foundation Grants DMS 0300806 and 0404547.     

On Statistical Inference Based on Record Values

We develop methodology for conducting inference based on record values and record times derived from a sequence of independent and identically distributed random variables. The advantage of using information about record times as well as record values is stressed. This point is a subtle one, since if the sampling distribution F is continuous then there is no information at all about F in the record times alone; the joint distribution of any number of them does not depend on F. However, the record times and record values jointly contain considerably more information about F than do the record values alone. Indeed, in the case of a distribution with regularly varying tails, the rate of convergence of the exponent of regular variation is two orders of magnitude faster if information about record times is included. Optimal estimators and convergence rates are derived under simple, specific models, and shown to be surprisingly robust against significant departures from those models. However, even under our special models the estimators have irregular properties, including an undefined information matrix. To some extent these difficulties may be alleviated by conditioning and by considering the relationship between maximum likelihood and maximum probability estimators.