Admissible predictive density estimation

By Lawrence D. Brown, Edward I. George. 2008

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Let Xj Np(;v xI) and Y j Np(;v yI) be independent p-dimensional multivariate normal vectors with common unknown mean . Based on observing X = x, we consider the problem of estimating the true predictive density p(yj ) 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 (1982) are sucient for a formal Bayes rule to be admissible. 1. Introduction. Let Xj Np(;v xI) and Yj Np(;v yI) be independent p-dimensional multivariate normal vectors with a common unknown mean 2 R p . We assume that vx > 0 and vy > 0 are known. We let p(xj ) and p(yj ) denote the conditional densities of X and Y , suppressing the dependence onvx and vy throughout. Based on observing only X = x, we consider the problem of estimating the density p(yj ) of Y . The natural action spaceA0 consists of all proper densities on R p , i.e.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0951d3ca547df9e6241515fc5179500ed551c478