Date of this Version
The Annals of Statistics
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.
The original and published work is available at: https://projecteuclid.org/euclid.aos/1211819560#abstract
admissibility, Bayesian predictive distribution, complete class, prior distributions
Brown, L. D., George, E. I., & Xu, X. (2008). Admissible Predictive Density Estimation. The Annals of Statistics, 36 (3), 1156-1170. http://dx.doi.org/10.1214/07-AOS506
Date Posted: 27 November 2017
This document has been peer reviewed.