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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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    1. Tong, Tiejun & Wang, Yuedong, 2007. "Optimal Shrinkage Estimation of Variances With Applications to Microarray Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 113-122, March.
    2. Smyth Gordon K, 2004. "Linear Models and Empirical Bayes Methods for Assessing Differential Expression in Microarray Experiments," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-28, February.
    3. Jiaying Gu & Roger Koenker, 2017. "Rebayes: an R package for empirical bayes mixture methods," CeMMAP working papers CWP37/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Jiaying Gu & Roger Koenker, 2017. "Rebayes: an R package for empirical bayes mixture methods," CeMMAP working papers 37/17, Institute for Fiscal Studies.
    5. J. T. Gene Hwang & Jing Qiu & Zhigen Zhao, 2009. "Empirical Bayes confidence intervals shrinking both means and variances," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 265-285, January.
    6. Haff, L. R., 1977. "Minimax estimators for a multinormal precision matrix," Journal of Multivariate Analysis, Elsevier, vol. 7(3), pages 374-385, September.
    7. Roger Koenker & Ivan Mizera, 2014. "Convex Optimization, Shape Constraints, Compound Decisions, and Empirical Bayes Rules," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 674-685, June.
    8. Daniel Yekutieli, 2012. "Adjusted Bayesian inference for selected parameters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(3), pages 515-541, June.
    9. Pan, Jia-Chiun & Huang, Yufen & Hwang, J.T. Gene, 2017. "Estimation of selected parameters," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 45-63.
    10. Champion, Colin J., 2003. "Empirical Bayesian estimation of normal variances and covariances," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 60-79, October.
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