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October 2020 Proper Bayes minimax estimation of parameters of Poisson distributions in the presence of unbalanced sample sizes
Yasuyuki Hamura, Tatsuya Kubokawa
Braz. J. Probab. Stat. 34(4): 728-751 (October 2020). DOI: 10.1214/19-BJPS459

Abstract

In this paper, we consider the problem of simultaneously estimating parameters of independent Poisson distributions in the presence of possibly unbalanced sample sizes under weighted standardized squared error loss. A class of heterogeneous Bayesian shrinkage estimators that utilize the unbalanced nature of sample sizes is proposed. To provide a theoretical justification, we first derive a necessary and sufficient condition for an estimator in the class to be proper Bayes and hence admissible and then obtain sufficient conditions for minimaxity that are compatible with the admissibility condition. Heterogeneous and homogeneous shrinkage estimators are compared by simulation. Several estimation methods are applied to data relating to the standardized mortality ratio.

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Yasuyuki Hamura. Tatsuya Kubokawa. "Proper Bayes minimax estimation of parameters of Poisson distributions in the presence of unbalanced sample sizes." Braz. J. Probab. Stat. 34 (4) 728 - 751, October 2020. https://doi.org/10.1214/19-BJPS459

Information

Received: 1 October 2018; Accepted: 1 September 2019; Published: October 2020
First available in Project Euclid: 25 September 2020

MathSciNet: MR4153639
Digital Object Identifier: 10.1214/19-BJPS459

Rights: Copyright © 2020 Brazilian Statistical Association

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Vol.34 • No. 4 • October 2020
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