Admissible predictive density estimation
成果类型：
Article
署名作者：
Brown, Lawrence D.; George, Edward I.; Xu, Xinyi
署名单位：
University of Pennsylvania; University System of Ohio; Ohio State University
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/07-AOS506
发表日期：
2008
页码：
1156-1170
关键词：
摘要：
Let X vertical bar mu similar to N-p (mu, upsilon I-x) and Y vertical bar mu similar to N-p (mu, upsilon I-y) be independent p-dimensional multivariate normal vectors with common unknown mean A. Based on observing X = x, we consider the problem of estimating the true predictive density p(y vertical bar mu) of Y under expected Kullback-Leibler loss. Our focus here is the characterization of admissible procedures for this problem. We show that the class of all generalized Bayes rules is a complete class, and that the easily interpretable conditions of Brown and Hwang [Statistical Decision Theory and Related Topics (1982) III 205-230] are sufficient for a formal Bayes rule to be admissible.