Open Access
VOL. 8 | 2012 Bayesian predictive densities for linear regression models under α-divergence loss: Some results and open problems
Yuzo Maruyama, William E. Strawderman

Editor(s) Dominique Fourdrinier, Éric Marchand, Andrew L. Rukhin

Inst. Math. Stat. (IMS) Collect., 2012: 42-56 (2012) DOI: 10.1214/11-IMSCOLL803


This paper considers estimation of the predictive density for a normal linear model with unknown variance under α-divergence loss for 1α1. We first give a general canonical form for the problem, and then give general expressions for the generalized Bayes solution under the above loss for each α. For a particular class of hierarchical generalized priors studied in Maruyama and Strawderman (2005, 2006) for the problems of estimating the mean vector and the variance respectively, we give the generalized Bayes predictive density. Additionally, we show that, for a subclass of these priors, the resulting estimator dominates the generalized Bayes estimator with respect to the right invariant prior, i.e., the best (fully) equivariant minimax estimator when α=1.


Published: 1 January 2012
First available in Project Euclid: 14 March 2012

zbMATH: 1326.62021
MathSciNet: MR3202501

Digital Object Identifier: 10.1214/11-IMSCOLL803

Primary: 62C20 , 62J07
Secondary: 62F15

Keywords: alpha-divergence , Bayesian predictive density , shrinkage prior , Stein effect

Rights: Copyright © 2012, Institute of Mathematical Statistics

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