文章基本信息

标题：Integral Inequality for Minimaxity in the Stein Problem
本地全文：下载
作者：Tatsuya Kubokawa
期刊名称：JOURNAL OF THE JAPAN STATISTICAL SOCIETY
印刷版ISSN：1882-2754
电子版ISSN：1348-6365
出版年度：2009
卷号：39
期号：2
页码：155-175
DOI：10.14490/jjss.39.155
出版社：JAPAN STATISTICAL SOCIETY
摘要：In the estimation of a multivariate normal mean, it is shown that the problem of deriving shrinkage estimators improving on the maximum likelihood estimator can be reduced to that of solving an integral inequality. The integral inequality not only provides a more general condition than a conventional differential inequality studied in the literature, but also handles non-differentiable or discontinuous estimators. The paper also gives general conditions on prior distributions such that the resulting generalized Bayes estimators are minimax. Finally, a simple proof for constructing a class of estimators improving on the James-Stein estimator is given based on the integral expression of the risk.
关键词：Decision theory;differential inequality;estimation;inadmissibility;integral inequality;James-Stein estimator;linear regression model;normal distribution;regression coefficients;risk function;uniform domination