Admissible Predictive Density Estimation 1

Let X|μ ∼ Np(μ,vxI ) and Y |μ ∼ Np(μ,vyI ) be independent pdimensional 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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