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Admissible predictive density estimation
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DOI：10.1214/07-AOS506.png)
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Abstract
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Let X vertical bar mu similar to N-p (mu, upsilon I-x) and Y vertical bar mu similar to N-p (mu, upsilon I-y) be independent p-dimensional multivariate normal vectors with common unknown mean A. Based on observing X = x, we consider the problem of estimating the true predictive density p(y vertical bar mu) 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.
Keywords:
admissibility
Bayesian predictive distribution
complete class
prior distributions
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