Proper Bayes minimax estimators of the normal mean matrix with common unknown variances

被引:5
作者
Tsukuma, Hisayuki [1 ]
机构
[1] Toho Univ, Fac Med, Ota Ku, Tokyo 1438540, Japan
关键词
Admissibility; Decision theory; Equivariance; Generalized Bayes estimation; Hierarchical model; Minimaxity; Quadratic loss; Shrinkage estimator; ADMISSIBILITY; INEQUALITIES; VECTOR;
D O I
10.1016/j.jspi.2010.03.031
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
This paper addresses the problem of estimating a matrix of the normal means, where the variances are unknown but common. The approach to this problem is provided by a hierarchical Bayes modeling for which the first stage prior for the means is matrix-variate normal distribution with mean zero matrix and a covariance structure and the second stage prior for the covariance is similar to Jeffreys' rule. The resulting hierarchical Bayes estimators relative to the quadratic loss function belong to a class of matricial shrinkage estimators. Certain conditions are obtained for admissibility and minimaxity of the hierarchical Bayes estimators. (C) 2010 Elsevier B.V. All rights reserved.
引用
收藏
页码:2596 / 2606
页数:11
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