Finite sample inference for empirical Bayesian methods

Nguyen, H. D. and Gupta, M. (2023) Finite sample inference for empirical Bayesian methods. Scandinavian Journal of Statistics, (doi: 10.1111/sjos.12643) (Early Online Publication)

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 of Wasserman et al. (2020), 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.

• Item Type: Articles
• Additional Information: Research Funding: Australian Research Council.
• Status: Early Online Publication
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Gupta, Professor Mayetri
• Authors: Nguyen, H. D., and Gupta, M.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Journal Name: Scandinavian Journal of Statistics
• Publisher: Wiley
• ISSN: 0303-6898
• ISSN (Online): 1467-9469
• Published Online: 28 March 2023
• Copyright Holders: Copyright © 2023 The Authors
• First Published: First published in Scandinavian Journal of Statistics 2023
• Publisher Policy: Reproduced under a Creative Commons license

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