統計学輪講（第２５回）

統計学輪講（第25回）
日時      2015年01月13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    Éric Marchand (Université de Sherbrooke)
演題      On Predictive Density Estimation under Integrated L_2 and L_1 losses

概要
Our investigation concerns the estimation of predictive densities and the efficiency as measured by frequentist risk of such predictive densities with integrated L2 and L_1 losses.   After introducing the problem and reviewing previous results for Kullback-Leibler loss relative to Bayes estimators, plug-in estimators and  multivariate normal models, I will begin by discussing L2 and L1 results concerning Bayesian estimation, best equivariant estimation, and minimax estimation.   As well, we will focus on the performance of  plug-in type estimators with improvements obtained by expansion of the variance, and a duality result (in the normal case) with a point estimation problem bringing into play reflected normal loss.   In the multivariate normal case in three of more dimensions, we show that the MRE estimator is inadmissible under L2 loss and provide dominating estimators.  This brings into play Stein-type results for estimating a multivariate normal mean.  Finally, we describe analogous results for spherically symmetric distributions and/or for L1 loss.   
This is joint, and still ongoing, work with Tatsuya Kubokawa (University of Tokyo) and Bill Strawderman (Rutgers University).