Empirical Bayes predictive densities for high-dimensional normal models

Xinyi Xu and Dunke Zhou

Journal of Multivariate Analysis, 2011, vol. 102, issue 10, 1417-1428

Abstract: This paper addresses the problem of estimating the density of a future outcome from a multivariate normal model. We propose a class of empirical Bayes predictive densities and evaluate their performances under the Kullback-Leibler (KL) divergence. We show that these empirical Bayes predictive densities dominate the Bayesian predictive density under the uniform prior and thus are minimax under some general conditions. We also establish the asymptotic optimality of these empirical Bayes predictive densities in infinite-dimensional parameter spaces through an oracle inequality.

Keywords: Predictive; density; Kullback-Leibler; loss; Empirical; Bayes; Minimaxity; Oracle; inequality; Shrinkage; estimation (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (1)

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