The Annals of Statistics

Admissible predictive density estimation

Lawrence D. Brown, Edward I. George, and Xinyi Xu

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 36, Number 3 (2008), 1156-1170.

Dates
First available in Project Euclid: 26 May 2008

Permanent link to this document
https://projecteuclid.org/euclid.aos/1211819560

Digital Object Identifier
doi:10.1214/07-AOS506

Mathematical Reviews number (MathSciNet)
MR2418653

Zentralblatt MATH identifier
1216.62012

Subjects
Primary: 62C15: Admissibility
Secondary: 62C07: Complete class results 62C10: Bayesian problems; characterization of Bayes procedures 62C20: Minimax procedures

Keywords
Admissibility Bayesian predictive distribution complete class prior distributions

Citation

Brown, Lawrence D.; George, Edward I.; Xu, Xinyi. Admissible predictive density estimation. Ann. Statist. 36 (2008), no. 3, 1156--1170. doi:10.1214/07-AOS506. https://projecteuclid.org/euclid.aos/1211819560


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