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Empirical Bayes When Estimation Precision Predicts Parameters

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  • Jiafeng Chen

Abstract

Gaussian empirical Bayes methods usually maintain a precision independence assumption: The unknown parameters of interest are independent from the known standard errors of the estimates. This assumption is often theoretically questionable and empirically rejected. This paper proposes to model the conditional distribution of the parameter given the standard errors as a flexibly parametrized location-scale family of distributions, leading to a family of methods that we call CLOSE. The CLOSE framework unifies and generalizes several proposals under precision dependence. We argue that the most flexible member of the CLOSE family is a minimalist and computationally efficient default for accounting for precision dependence. We analyze this method and show that it is competitive in terms of the regret of subsequent decisions rules. Empirically, using CLOSE leads to sizable gains for selecting high-mobility Census tracts.

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  • Jiafeng Chen, 2022. "Empirical Bayes When Estimation Precision Predicts Parameters," Papers 2212.14444, arXiv.org, revised Dec 2024.
    • Handle: RePEc:arx:papers:2212.14444
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    References listed on IDEAS

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    1. Xianchao Xie & S. C. Kou & Lawrence D. Brown, 2012. "SURE Estimates for a Heteroscedastic Hierarchical Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1465-1479, December.
    2. Koenker, Roger & Mizera, Ivan, 2014. "Convex Optimization in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 60(i05).
    3. 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.
    4. Asaf Weinstein & Zhuang Ma & Lawrence D. Brown & Cun-Hui Zhang, 2018. "Group-Linear Empirical Bayes Estimates for a Heteroscedastic Normal Mean," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 698-710, April.
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    Cited by:

    1. Jiafeng Chen, 2023. "On the robustness of posterior means," Papers 2303.08653, arXiv.org, revised Dec 2024.
    2. Stephane Bonhomme & Angela Denis, 2024. "Estimating Heterogeneous Effects: Applications to Labor Economics," Papers 2404.01495, arXiv.org.
    3. Andreas Petrou-Zeniou & Azeem M. Shaikh, 2024. "Inference on Multiple Winners with Applications to Microcredit and Economic Mobility," Papers 2410.19212, arXiv.org.

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