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Robust Empirical Bayes Confidence Intervals

Author

Listed:
  • Timothy B. Armstrong

    (University of Southern California)

  • Michal Kolesár

    (Princeton University)

  • Mikkel Plagborg-Møller

    (Princeton University)

Abstract

We construct robust empirical Bayes confidence intervals (EBCIs) in a normal means problem. The intervals are centered at the usual linear empirical Bayes estimator, but use a critical value accounting for shrinkage. Parametric EBCIs that assume a normal distribution for the means (Morris, 1983b) may substantially undercover when this assumption is violated. In contrast, our EBCIs control coverage regardless of the means distribution, while remaining close in length to the parametric EBCIs when the means are indeed Gaussian. If the means are treated as fixed, our EBCIs have an average coverage guarantee: the coverage probability is at least 1−α on average across the n EBCIs for each of the means. Our empirical application considers the effects of U.S. neighborhoods on intergenerational mobility.

Suggested Citation

  • Timothy B. Armstrong & Michal Kolesár & Mikkel Plagborg-Møller, 2022. "Robust Empirical Bayes Confidence Intervals," Working Papers 2022-27, Princeton University. Economics Department..
    • Handle: RePEc:pri:econom:2022-27
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    File URL: https://www.princeton.edu/~mkolesar/papers/ebci.pdf
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    References listed on IDEAS

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    1. Evan T.R. Rosenman & Guillaume Basse & Art B. Owen & Mike Baiocchi, 2023. "Combining observational and experimental datasets using shrinkage estimators," Biometrics, The International Biometric Society, vol. 79(4), pages 2961-2973, December.
    2. Boot, Tom, 2023. "Joint inference based on Stein-type averaging estimators in the linear regression model," Journal of Econometrics, Elsevier, vol. 235(2), pages 1542-1563.

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    More about this item

    Keywords

    average coverage; empirical Bayes; confidence interval; shrinkage;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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