Empirical Bayes predictive densities for high-dimensional normal models

Authors:
Xinyi Xu;Dunke Zhou
Affiliations:
-;-
Venue:
Journal of Multivariate Analysis
Year:
2011

Citing 5
Cited 0

Statistical analysis with missing data

Statistical analysis with missing data
Entropy Inference and the James-Stein Estimator, with Application to Nonlinear Gene Association Networks

The Journal of Machine Learning Research
The minimum description length principle in coding and modeling

IEEE Transactions on Information Theory
An information criterion for likelihood selection

IEEE Transactions on Information Theory
Exact minimax strategies for predictive density estimation, data compression, and model selection

IEEE Transactions on Information Theory

Quantified Score

Hi-index	0.00

Visualization

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.