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Empirical Bayes When Estimation Precision Predicts Parameters

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  • Jiafeng Chen

Abstract

Empirical Bayes methods usually maintain a prior 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 instead models the conditional distribution of the parameter given the standard errors as a flexibly parametrized family of distributions, leading to a family of methods that we call CLOSE. This paper establishes that (i) CLOSE is rate-optimal for squared error Bayes regret, (ii) squared error regret control is sufficient for an important class of economic decision problems, and (iii) CLOSE is worst-case robust when our assumption on the conditional distribution is misspecified. Empirically, using CLOSE leads to sizable gains for selecting high-mobility Census tracts. Census tracts selected by CLOSE are substantially more mobile on average than those selected by the standard shrinkage method.

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  • Jiafeng Chen, 2022. "Empirical Bayes When Estimation Precision Predicts Parameters," Papers 2212.14444, arXiv.org, revised Apr 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. "Mean-variance constrained priors have finite maximum Bayes risk in the normal location model," Papers 2303.08653, arXiv.org.
    2. Stephane Bonhomme & Angela Denis, 2024. "Estimating Heterogeneous Effects: Applications to Labor Economics," Papers 2404.01495, arXiv.org.

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