Generalized Bayes minimax estimators of the mean of multivariate normal distribution with unknown variance

被引：12

作者：

Wells, Martin T. ^{[1
]}

Zhou, Gongfu ^{[2
]}

机构：

[1] Cornell Univ, Dept Stat Sci, Ithaca, NY 14853 USA

[2] Yale Univ, Dept Epidemiol & Publ Hlth, New Haven, CT 06520 USA

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 2008年 / 99卷 / 10期

关键词：

Generalized Bayes estimate; Integration by parts; Minimax estimate; Multivariate normal mean; Invariant loss; Unknown variance; Weakly differentiable function;

D O I：

10.1016/j.jmva.2008.02.016

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：

We construct a broad class of generalized Bayes minimax estimators of the mean of a multivariate normal distribution with covariance equal to sigma I-2(p), with sigma(2) unknown, and under the invariant loss parallel to delta(X) - theta parallel to(2)/sigma(2). Examples that illustrate the theory are given. Most notably it is shown that a hierarchical version of the multivariate Student-t prior yields a Bayes minimax estimate. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：2208 / 2220

页数：13

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