統計学輪講（第17回） 日時 2012年10月23日(火) 14時50分～16時30分 場所 経済学部新棟３階第３教室 講演者 Eric Marchand (Universite de Sherbrooke) 演題 On improved predictive density estimation with parametric constraints 概要 We consider the problem of predictive density estimation under Kullback-Leibler loss when the parameter space is restricted. The principal situation analyzed relates to the estimation of an unknown predictive p-variate normal density based on an observation generated by another p-variate normal density. The means of the densities are assumed to coincide, the covariance matrices are a known multiple of the identity matrix. We obtain sharp results concerning plug-in estimators, we show that the best unrestricted invariant predictive density estimator is dominated by the Bayes estimator associated with a uniform prior on the restricted parameter space, and we obtain minimax results for cases where the parameter space is (i) a cone, and (ii) a ball. A key feature, which we will describe, is a correspondence between the predictive density estimation problem with a collection of point estimation problems. Finally, we describe recent results including recent work in collaboration with Tatsuya Kubokawa, Bill Strawderman and Jean-Philippe Turcotte.