增长曲线模型中存在UMRE估计的充要条件

对于协方差阵任意或具有均匀结构或具有序列结构的正态增长曲线模型,在仿射变换群和转移交换群、二次损失和矩阵损失下,分别获得了存在回归系数矩阵的一致最小风险同变(UMRE)估计的充要条件.     

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．     

增长曲线模型中一致最小风险无偏估计的存在性

考虑协方差阵任意，或具有均匀协方差结构，或具有序列协方差结构的正态增长曲线模型本文将文[19]在设计矩阵满秩，且仅估计回归系数矩阵的情形获得的结果推广到设计矩阵不必列满秩，且同时估计回归系数矩阵的线性可估函数和协方差阵（或有关参数）的情形；在凸损失函数类和矩阵损失函数下，给出存在一致最小风险无偏估计的充分必要条件．     

一类正态线性模型中参数的一致最小风险同变估计的存在性

研究了一类正态线性模型参数的一致最小风险同变(UMRE)估计的存在性. 这类模型包含了正态方差分量模型、增长曲线模型、 扩充的增长曲线模型以及似乎不相关回归方程组等. 在这类模型、仿射变换群、二次损失或矩阵损失下, 分别导出了回归系数的线性可估函数、协方差阵V和(trV)α(α>0已知)的UMRE估计存在的充分必要条件. 利用这些结果可导出文献中有关(扩充)增长曲线模型和似乎不相关回归方程组中估计回归系数的结果,并把协方差阵V和trV的UMRE估计不存在的充分条件发展成充分必要条件. 此外, 导出了方差分量模型中参数的UMRE估计存在的充分必要条件.     

SURE模型中参数的UMRE估计的一个注记

本文考虑似乎不相关回归方程组（ＳＵＲＥ）模型在设计阵不满秩情形下回归系数的一致最小风险同变（ＵＭＲＥ）估计。给出仿射变换群，转移变换群各自在二次损失和矩阵损失下回归系数可估函数存在ＵＭＲＥ估计的充要条件。     

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.     

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.     

常用正态协方差阵估计的非容许性

在二次损失函数下,本文给出了正态方差最优同变估计的一个新的改进估计,并证明了常用正态协方差和协方差阵的估计都是非容许估计。     

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．     

一般Gauss-Markov模型中可估函数的线性Minimax估计

设Y是具有均值Xβ和协方差阵σ2V的n维随机向量,Sβ是线性可估函数,这里X,S和V≥0是已知矩阵,β∈Rp和σ2＞0是未知参数.本文分别在给定的矩阵损失和二次损失下研究了线性估计的Minimax性.在适当的假设下,得到了Sβ的唯一线性Minimax估计(有关唯一性在几乎处处意义下理解).     

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.     

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。     

A Generalization of Rao's Covariance Structure with Applications to Several Linear Models

This paper presents a generalization of Rao's covariance structure. In a general linear regression model, we classify the error covariance structure into several categories and investigate the efficiency of the ordinary least squares estimator (OLSE) relative to the Gauss–Markov estimator (GME). The classification criterion considered here is the rank of the covariance matrix of the difference between the OLSE and the GME. Hence our classification includes Rao's covariance structure. The results are applied to models with special structures: a general multivariate analysis of variance model, a seemingly unrelated regression model, and a serial correlation model.     

Estimation of means of multivariate normal populations with order restriction

Multivariate isotonic regression theory plays a key role in the field of statistical inference under order restriction for vector valued parameters. Two cases of estimating multivariate normal means under order restricted set are considered. One case is that covariance matrices are known, the other one is that covariance matrices are unknown but are restricted by partial order. This paper shows that when covariance matrices are known, the estimator given by this paper always dominates unrestricted maximum likelihood estimator uniformly, and when covariance matrices are unknown, the plug-in estimator dominates unrestricted maximum likelihood estimator under the order restricted set of covariance matrices. The isotonic regression estimators in this paper are the generalizations of plug-in estimators in unitary case.     

A Note on Random Effects Growth Curve Models

The robustness of regression coefficient estimator is a hot topic in regression analysis all the while. Since the response observations are not independent, it is extraordinarily difficult to study this problem for random effects growth curve models, especially when the design matrix is non-full of rank. The paper not only gives the necessary and sufficient conditions under which the generalized least square estimate is identical to the the best linear unbiased estimate when error covariance matrix is an arbitrary positive definite matrix, but also obtains a concise condition under which the generalized least square estimate is identical to the maximum likelihood estimate when the design matrix is full or non-full of rank respectively. In addition, by using of the obtained results, we get some corollaries for the the generalized least square estimate be equal to the maximum likelihood estimate under several common error covariance matrix assumptions. Illustrative examples for the case that the design matrix is full or non-full of rank are also given.     

Asymptotic distribution of the weighted least squares estimator

This paper derives the asymptotic distribution of the weighted least squares estimator (WLSE) in a heteroscedastic linear regression model. A consistent estimator of the asymptotic covariance matrix of the WLSE is also obtained. The results are obtained under weak conditions on the design matrix and some moment conditions on the error distributions. It is shown that most of the error distributions encountered in practice satisfy these moment conditions. Some examples of the asymptotic covariance matrices are also given.     

平衡损失下一般Gauss-Markov模型中回归系数的最优估计（英文）

在平衡损失下,我们研究了一般Gauss-Markov模型中回归系数的最优估计,首先我们得到了线性估计为最佳线性无偏估计的充分必要条件;其次证明了平衡损失下的最佳线性无偏估计在几乎处处意义下是唯一的,并且是普通最小二乘估计和二次损失下最优估计的平衡;最后,我们讨论了最优估计关于损失函数和模型设定的稳健性,并得到了该最优估计在模型误定下具有稳健性的充分必要条件.