Predictive Density Estimation for Multivariate Normal and Spherically Symmetric Densities

• Activity Number: 569 - Recent Advances in Predictive Inference
• Type: Topic Contributed
• Date/Time: Wednesday, August 2, 2017 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Eric Marchand*
• Companies: Universite De Sherbrooke
• Keywords: Predictive density ; Kullback-Leibler ; Multivariate normal ; Spherically symmetric ; Dominance

Abstract

Based on a sample drawn from a multivariate normal population, we consider the estimation of a predictive density for a future multivariate normal observable and measure efficiency by Kullback-Leibler risk. We provide improvements on the benchmark minimum risk equivariant predictive density in three dimensions or more. We present one approach which also leads to a dual point prediction problem of interest on its own. The dominance results are shown to be robust with respect to a wide class of spherically symmetric model departures from normality. Finally, Bayesian improvements are obtained for the non-normal case, thus extending normal case findings of Kato (2009), as well as Boisbunon and Maruyama (2014).