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arXiv · 0806.2914

Admissible predictive density estimation

Lawrence D. Brown·Edward I. George·Xinyi Xu
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Abstract

Let $X|μ\sim N_p(μ,v_xI)$ and $Y|μ\sim N_p(μ,v_yI)$ 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.

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Lawrence D. Brown, Edward I. George, Xinyi Xu. 2008-06-18. Admissible predictive density estimation. https://doi.org/10.1214/07-aos506

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