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On F-modelling-based empirical Bayes estimation of variances

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  • Yeil Kwon
  • Zhigen Zhao

Abstract

SummaryWe consider the problem of empirical Bayes estimation of multiple variances when provided with sample variances. Assuming an arbitrary prior on the variances, we derive different versions of the Bayes estimators using different loss functions. For one particular loss function, the resulting Bayes estimator relies on the marginal cumulative distribution function of the sample variances only. When replacing it with the empirical distribution function, we obtain an empirical Bayes version called the $F$-modelling-based empirical Bayes estimator of variances. We provide theoretical properties of this estimator, and further demonstrate its advantages through extensive simulations and real data analysis.

Suggested Citation

  • Yeil Kwon & Zhigen Zhao, 2023. "On F-modelling-based empirical Bayes estimation of variances," Biometrika, Biometrika Trust, vol. 110(1), pages 69-81.
    • Handle: RePEc:oup:biomet:v:110:y:2023:i:1:p:69-81.
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    File URL: http://hdl.handle.net/10.1093/biomet/asac019
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    References listed on IDEAS

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