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Admissible predictive density estimation. (English) Zbl 1216.62012
Summary: Let \(X|\mu \sim N_p(\mu , v_xI)\) and \(Y|\mu \sim N_p(\mu , v_yI)\) be independent \(p\)-dimensional multivariate normal vectors with common unknown mean \(\mu \). Based on observing \(X=x\), we consider the problem of estimating the true predictive density \(p(y|\mu )\) 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 L.D. Brown and J.T. Hwang [Statistical decision theory and related topics III, 205–230 (1982; Zbl 0585.62016)] are sufficient for a formal Bayes rule to be admissible.

MSC:
62C15 Admissibility in statistical decision theory
62C07 Complete class results in statistical decision theory
62C10 Bayesian problems; characterization of Bayes procedures
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