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Nearly minimax empirical Bayesian prediction of independent Poisson observables

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  • Li, Xiao

Abstract

In this study, simultaneous predictive distributions for independent Poisson observables are considered and the performance of predictive distributions is evaluated using the Kullback–Leibler (K–L) loss. This study proposes a class of empirical Bayesian predictive distributions that dominate the Bayesian predictive distribution based on the Jeffreys prior. The K–L risk of the empirical Bayesian predictive distributions is demonstrated to be less than 1.04 times the minimax lower bound.

Suggested Citation

  • Li, Xiao, 2024. "Nearly minimax empirical Bayesian prediction of independent Poisson observables," Statistics & Probability Letters, Elsevier, vol. 208(C).
    • Handle: RePEc:eee:stapro:v:208:y:2024:i:c:s0167715224000440
    DOI: 10.1016/j.spl.2024.110075
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    References listed on IDEAS

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    1. 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.
    2. Komaki, Fumiyasu, 2006. "A class of proper priors for Bayesian simultaneous prediction of independent Poisson observables," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1815-1828, September.
    3. Takeru Matsuda & Fumiyasu Komaki, 2015. "Singular value shrinkage priors for Bayesian prediction," Biometrika, Biometrika Trust, vol. 102(4), pages 843-854.
    4. Yasuyuki Hamura & Tatsuya Kubokawa, 2020. "Bayesian predictive distribution for a Poisson model with a parametric restriction," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(13), pages 3257-3266, July.
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