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2022 Poisson mean vector estimation with nonparametric maximum likelihood estimation and application to protein domain data
Hoyoung Park, Junyong Park
Author Affiliations +
Electron. J. Statist. 16(2): 3789-3835 (2022). DOI: 10.1214/22-EJS2029

Abstract

In this paper, we propose the nonparametric empirical Bayes (NPEB) estimator based on the nonparametric maximum likelihood estimation (NPMLE) in Poisson mean vector estimation, also known as the g-modeling in the nonparametric empirical Bayes method. Due to the recent developments of highly scalable algorithms of empirical Bayes, it is more attractive to use g-modelling, while most of the studies have focused on the performance of f-modeling in the NPEB estimator. We study the theoretical properties of the NPEB estimator of Poisson mean vector based on g-modeling combined with the NPMLE, such as the convergence rate, and compare our result with some existing studies. Our simulation studies and real data examples of protein domain data show that the estimator based on the g-modeling outperforms existing f-modeling based estimators in both computational efficiency and accuracy.

Funding Statement

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2C1A01100526).

Acknowledgments

We are grateful to two referees and the editor, whose valuable suggestions and comments have greatly improved the presentation of the paper. Research of J. Park was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2C1A01100526).

Citation

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Hoyoung Park. Junyong Park. "Poisson mean vector estimation with nonparametric maximum likelihood estimation and application to protein domain data." Electron. J. Statist. 16 (2) 3789 - 3835, 2022. https://doi.org/10.1214/22-EJS2029

Information

Received: 1 August 2021; Published: 2022
First available in Project Euclid: 13 July 2022

Digital Object Identifier: 10.1214/22-EJS2029

Subjects:
Primary: 62G05
Secondary: 62C12 , 62C25

Keywords: Compound decision problem , Empirical Bayes , nonparametric maximum likelihood estimate , Poisson distribution

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Vol.16 • No. 2 • 2022
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