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Empirical Bayes predictive densities for high-dimensional normal models

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  • Xu, Xinyi
  • Zhou, Dunke

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.

Suggested Citation

  • Xu, Xinyi & Zhou, Dunke, 2011. "Empirical Bayes predictive densities for high-dimensional normal models," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1417-1428, November.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:10:p:1417-1428
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    References listed on IDEAS

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    1. Miller, Don M. & Williams, Dan, 2003. "Shrinkage estimators of time series seasonal factors and their effect on forecasting accuracy," International Journal of Forecasting, Elsevier, vol. 19(4), pages 669-684.
    2. George, Edward I. & Xu, Xinyi, 2008. "Predictive Density Estimation For Multiple Regression," Econometric Theory, Cambridge University Press, vol. 24(2), pages 528-544, April.
    3. Weinberg, Jonathan & Brown, Lawrence D. & Stroud, Jonathan R., 2007. "Bayesian Forecasting of an Inhomogeneous Poisson Process With Applications to Call Center Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1185-1198, December.
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    Cited by:

    1. Li, Xiao, 2024. "Nearly minimax empirical Bayesian prediction of independent Poisson observables," Statistics & Probability Letters, Elsevier, vol. 208(C).

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