統計学輪講（第１７回）

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.