Admissible predictive density estimation
Lawrence D. Brown, Edward I. George, and Xinyi Xu
Source: Ann. Statist. Volume 36, Number 3 (2008), 1156-1170.
Abstract
Let X|μ∼Np(μ, vxI) and Y|μ∼Np(μ, vyI) be independent p-dimensional multivariate normal vectors with common unknown mean μ. Based on observing X=x, we consider the problem of estimating the true predictive density p(y|μ) 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.
Primary Subjects: 62C15
Secondary Subjects: 62C07, 62C10, 62C20
Keywords: Admissibility; Bayesian predictive distribution; complete class; prior distributions
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Permanent link to this document: http://projecteuclid.org/euclid.aos/1211819560
Digital Object Identifier: doi:10.1214/07-AOS506
Mathematical Reviews number (MathSciNet):
MR2418653
Zentralblatt MATH identifier:
05294969
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