Admissible predictive density estimation

Abstract

Let X|μ ∼ Np(μ, vx1) and Y|μ ∼ Np(μ,vy1) 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. © Institute of Mathematical Statistics, 2008.