Admissible predictive density estimation

Details Admissible predictive density estimation Admissible predictive density estimation

2008-06-18

arxiv.org/abs/0806.2914v1

Annals of Statistics 2008, Vol. 36, No. 3, 1156-1170

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-AOS506 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/07-AOS506

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 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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