简约SUR模型参数的协方差改进估计

考虑了SUR模型及其两个简约模型,给出简约模型下未知回归系数及其可估函数的协方差改进估计,并证明了在一定条件下该估计仍然是相应参数在原模型下的协方差改进估计.     

随机变量二次型的协方差在混合效应模型中的应用

本文提出方差分量ANOVA估计的一种改进方法, 证明了对于一般的方差分量模型, 只要方差分量的ANOVA估计存在就可以通过此方法给出其改进形式, 并且在均方误差意义下优于ANOVA估计. 特别地, 对于单向分类随机效应模型, Kelly和Mathew^[1]对ANOVA估计的改进就是我们提出的改进方法的特殊形式, 这也给出了此类改进估计在均方误差意义下优于ANOVA估计的另一种合理的解释. 同时, 本文又将此思想应用到对谱分解估计的改进上. 本文应用协方差的简单性质证明了对带有一个随机效应的方差分量模型, 当随机效应的协方差阵只有一个非零特征值时, 随机效应方差分量谱分解估计在均方误差意义下总是优于ANOVA估计. 本文最后将第三节的结论推广到广义谱分解估计下, 同时给出广义谱分解估计待定系数的一个合理的取值.     

平衡数据结构下ANOVA 估计和SD 估计的比较

在线性混合效应模型下, 方差分析(ANOVA) 估计和谱分解(SD) 估计对构造精确检验和广义P-值枢轴量起着非常重要的作用. 尽管这两估计分别基于不同的方法, 但它们共享许多类似的优点, 如无偏性和有精确的表达式等. 本文借助于已得到的协方差阵的谱分解结果, 揭示了平衡数据一般线性混合效应模型下ANOVA 估计与SD 估计的关系, 并分别针对协方差阵两种结构: 套结构和多项分类随机效应结构, 给出了ANOVA 估计与SD 估计等价的充分必要条件.     

包含多余回归变量的错误指定模型的随机约束Liu估计

对由于包含多余回归自变量而导致的错误指定线性回归模型,本文导出了回归系数的最小二乘估计,普通混合估计以及随机约束Liu估计,并在均方误差矩阵准则下对这三个估计的优良性进行了比较,给出了随机约束Liu估计优于最小二乘估计和普通混合估计的充要条件.此外,对它们所对应的经典预测值的优良性也进行了讨论.     

分块半相依线性回归模型的参数估计

考虑一般的分块半相依线性回归（SUR）模型及其相应的简约模型，给出简约模型下未知回归系数及其可估函数的协方差改进估计仍是分块SUR模型下相应参数的协方差改进估计的一个充要条件．     

增长曲线模型中UMRE估计的存在性

对于设计矩阵不满秩，协方差阵任意或具有均匀结构或序列结构的正态增长曲线模型，本文讨论参数矩阵的一致最小风险同变（UMng）估计的存在性．在仿射变换群GI和转移交换群、二次损失和矩阵损失下本文分别获得存在回归系数矩阵的线性可估函数矩阵的UMRE估计的充要条件，推广了由[21]给出的在设计矩阵满秩下估计回归系数矩阵的结果．本文还首次证明了在群G1和二次损失下不存在协方差阵V和trV的UMRE估计．     

部分线性模型的随机约束岭估计

研究了部分线性回归模型附加有随机约束条件时的估计问题.基于Profile最小二乘方法和混合估计方法提出了参数分量随机约束下的Profile混合估计,并研究了其性质.为了克服共线性问题,构造了参数分量的Profile混合岭估计,并给出了估计量的偏和方差.     

The rate of convergence for the least squares estimator in nonlinear regression model with dependent errors

We study the parameter estimation in a nonlinear regression model with a general error's structure,strong consistency and strong consistency rate of the least squares estimator are obtained.     

The Sample Covariance Is Not Efficient for Elliptical Distributions

It is well known that the sample covariance is not an efficient estimator of the covariance of a bivariate normal vector. We extend this result to elliptical distributions and we propose a simple explicit estimator, which is efficient in the normal case and which outperforms the sample covariance in general. Necessary and sufficient conditions are established under which this estimator is in general efficient for an elliptical distribution.     

Delete-group Jackknife Estimate in Partially Linear Regression Models with Heteroscedasticity

Abstract Consider a partially linear regression model with an unknown vector parameter β,an unknownfunction g(.),and unknown heteroscedastic error variances.Chen,You proposed a semiparametric generalizedleast squares estimator(SGLSE)for β,which takes the heteroscedasticity into account to increase efficiency.Forinference based on this SGLSE,it is necessary to construct a consistent estimator for its asymptotic covariancematrix.However,when there exists within-group correlation, the traditional delta method and the delete-1jackknife estimation fail to offer such a consistent estimator.In this paper, by deleting grouped partial residualsa delete-group jackknife method is examined.It is shown that the delete-group jackknife method indeed canprovide a consistent estimator for the asymptotic covariance matrix in the presence of within-group correlations.This result is an extension of that in[21].     

比例优势模型在多结局区间截断数据上的应用

探索比例优势模型在临床医学中常见的多结局区间截断数据中的应用.用条件的逻辑回归方法避免讨厌参数的估计,用牛顿-拉普森算法估计回归系数,用＂夹心方差＂估计量作为参数方差的估计.通过随机模型检验模型应用的有效性.     

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。     

带有结构变化的线性模型中参数估计的一些结果

本文在一些纯量损失和矩阵损失下研究带有结构变化的正态线性模型中参数的估计问题．分别给出 了存在回归系数的一致最小风险无偏（ＵＭＲＵ）估计和一致最小风险同变（ＵＭＲＥ）估计的充要条件, 证明了不存在误差方差在仿射变换群下的ＵＭＲＥ估计．导出了回归系数的最小二乘估计的可容许性 和极小极大性．     

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.     

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．     

A Dirichlet process functional approach to heteroscedastic-consistent covariance estimation

The mixture of Dirichlet process (MDP) defines a flexible prior distribution on the space of probability measures. This study shows that ordinary least-squares (OLS) estimator, as a functional of the MDP posterior distribution, has posterior mean given by weighted least-squares (WLS), and has posterior covariance matrix given by the (weighted) heteroscedastic-consistent sandwich estimator. This is according to a pairs bootstrap distribution approximation of the posterior, using a Pólya urn scheme. Also, when the MDP prior baseline distribution is specified as a product of independent probability measures, this WLS solution provides a new type of generalized ridge regression estimator. Such an estimator can handle multicollinear or singular design matrices even when the number of covariates exceeds the sample size, and can shrink the coefficient estimates of irrelevant covariates towards zero, which makes it useful for nonlinear regressions via basis expansions. Also, this MDP/OLS functional methodology can be extended to methods for analyzing the sensitivity of the heteroscedasticity-consistent causal effect size over a range of hidden biases, due to missing covariates omitted from the regression; and more generally, can be extended to a Vibration of Effects analysis. The methodology is illustrated through the analysis of simulated and real data sets. Overall, this study establishes new connections between Dirichlet process functional inference, the bootstrap, consistent sandwich covariance estimation, ridge shrinkage regression, WLS, and sensitivity analysis, to provide regression methodology useful for inferences of the mean dependent response.     

Estimation of the entropy of a multivariate normal distribution

Motivated by problems in molecular biosciences wherein the evaluation of entropy of a molecular system is important for understanding its thermodynamic properties, we consider the efficient estimation of entropy of a multivariate normal distribution having unknown mean vector and covariance matrix. Based on a random sample, we discuss the problem of estimating the entropy under the quadratic loss function. The best affine equivariant estimator is obtained and, interestingly, it also turns out to be an unbiased estimator and a generalized Bayes estimator. It is established that the best affine equivariant estimator is admissible in the class of estimators that depend on the determinant of the sample covariance matrix alone. The risk improvements of the best affine equivariant estimator over the maximum likelihood estimator (an estimator commonly used in molecular sciences) are obtained numerically and are found to be substantial in higher dimensions, which is commonly the case for atomic coordinates in macromolecules such as proteins. We further establish that even the best affine equivariant estimator is inadmissible and obtain Stein-type and Brewster–Zidek-type estimators dominating it. The Brewster–Zidek-type estimator is shown to be generalized Bayes.     

Estimating hazard ratios in nested case-control studies by mantel-haenszel method

1. IntroductionConsider a follow-up study which is carried out to investigate the association betweenexposure variables and mortality rate in a cohort. In the case where the cohort is of 1argesise, the complete follow-up ndght be too expensive or difficult, and various nested samplingmethod8 have been suggested by Thomas[l], Prenti..[2] 5 Goldstein and Langholzl'] and otherauthors. Most of the authors employ Coxl4] regression mode1 for estimating the hazard ratio8of exposures.Now a well-reco…     

Simultaneous estimation of means of classified normal observations

Simultaneous estimation of normal means is considered for observations which are classified into several groups. In a one-way classification case, it is shown that an adaptive shrinkage estimator dominates a Stein-type estimator which shrinks observations towards individual class averages as Stein's (1966,Festschrift for J. Neyman, (ed. F. N. David), 351–366, Wiley, New York) does, and is minimax even if class sizes are small. Simulation results under quadratic loss show that it is slightly better than Stein's (1966) if between variances are larger than within ones. Further this estimator is shown to improve on Stein's (1966) with respect to the Bayes risk. Our estimator is derived by assuming the means to have a one-way classification structure, consisting of three random terms of grand mean, class mean and residual. This technique can be applied to the case where observations are classified into a two-stage hierarchy.     

Iterative Weighted Semiparametric Least Squares Estimation in Repeated Measurement Partially Linear Regression Models

Consider a repeated measurement partially linear regression model with an unknown vector parameter β, an unknown function g(.), and unknown heteroscedastic error variances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of β, we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that it improves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given to determine the number of iterations. We also show that when the number of replicates is less than or equal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of those in [2] to the case of semiparametric regressions.