Uniform priors on convex sets improve risk

被引：23

作者：

Hartigan, JA ^{[1
]}

机构：

[1] Yale Univ, Dept Stat, New Haven, CT 06520 USA

来源：

STATISTICS & PROBABILITY LETTERS | 2004年 / 67卷 / 04期

基金：

美国国家科学基金会;

关键词：

uniform priors; Bayes estimators; squared error loss; improving risk; convex sets; multivariate normal;

D O I：

10.1016/j.spl.2004.01.009

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：

Let X be spherical normal with mean theta lying in a closed convex set C with a non-empty interior and a non-empty complement. For the prior distribution uniform over C, the mean squared error risk of the generalized Bayes estimator is less than or equal to that of X for theta is an element of C. It is equal to that of X if and only if C is a cone, and theta is an apex of the cone. (C) 2004 Elsevier B.V. All rights reserved.

引用

页码：285 / 288

页数：4

共 6 条

[1] MINIMAX ESTIMATION OF THE MEAN OF A NORMAL-DISTRIBUTION WHEN THE PARAMETER SPACE IS RESTRICTED [J].