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Finite sample inference for empirical Bayesian methods

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  • Hien Duy Nguyen
  • Mayetri Gupta

Abstract

In recent years, empirical Bayesian (EB) inference has become an attractive approach for estimation in parametric models arising in a variety of real‐life problems, especially in complex and high‐dimensional scientific applications. However, compared to the relative abundance of available general methods for computing point estimators in the EB framework, the construction of confidence sets and hypothesis tests with good theoretical properties remains difficult and problem specific. Motivated by the Universal Inference framework, we propose a general and universal method, based on holdout likelihood ratios, and utilizing the hierarchical structure of the specified Bayesian model for constructing confidence sets and hypothesis tests that are finite sample valid. We illustrate our method through a range of numerical studies and real data applications, which demonstrate that the approach is able to generate useful and meaningful inferential statements in the relevant contexts.

Suggested Citation

  • Hien Duy Nguyen & Mayetri Gupta, 2023. "Finite sample inference for empirical Bayesian methods," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(4), pages 1616-1640, December.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:4:p:1616-1640
    DOI: 10.1111/sjos.12643
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    References listed on IDEAS

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    Cited by:

    1. Dey, Neil & Martin, Ryan & Williams, Jonathan P., 2026. "Multiple testing in generalized universal inference," Statistics & Probability Letters, Elsevier, vol. 228(C).

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