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June 2008 Admissible predictive density estimation
Lawrence D. Brown, Edward I. George, Xinyi Xu
Ann. Statist. 36(3): 1156-1170 (June 2008). DOI: 10.1214/07-AOS506


Let X|μNp(μ, vxI) and Y|μNp(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.


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Lawrence D. Brown. Edward I. George. Xinyi Xu. "Admissible predictive density estimation." Ann. Statist. 36 (3) 1156 - 1170, June 2008.


Published: June 2008
First available in Project Euclid: 26 May 2008

zbMATH: 1216.62012
MathSciNet: MR2418653
Digital Object Identifier: 10.1214/07-AOS506

Primary: 62C15
Secondary: 62C07 , 62C10 , 62C20

Keywords: Admissibility , Bayesian predictive distribution , complete class , Prior distributions

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 3 • June 2008
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