June 2021 E-values: Calibration, combination and applications
Vladimir Vovk, Ruodu Wang
Author Affiliations +
Ann. Statist. 49(3): 1736-1754 (June 2021). DOI: 10.1214/20-AOS2020

Abstract

Multiple testing of a single hypothesis and testing multiple hypotheses are usually done in terms of p-values. In this paper, we replace p-values with their natural competitor, e-values, which are closely related to betting, Bayes factors and likelihood ratios. We demonstrate that e-values are often mathematically more tractable; in particular, in multiple testing of a single hypothesis, e-values can be merged simply by averaging them. This allows us to develop efficient procedures using e-values for testing multiple hypotheses.

Funding Statement

The first author was supported by Amazon, Astra Zeneca and Stena Line.
The second author was supported by NSERC grants RGPIN-2018-03823 and RGPAS-2018-522590.

Acknowledgments

The authors thank Aaditya Ramdas, Alexander Schied and Glenn Shafer for helpful suggestions. Thoughtful comments by the Associate Editor and four reviewers have led to numerous improvements in presentation and substance.

Citation

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Vladimir Vovk. Ruodu Wang. "E-values: Calibration, combination and applications." Ann. Statist. 49 (3) 1736 - 1754, June 2021. https://doi.org/10.1214/20-AOS2020

Information

Received: 1 December 2019; Revised: 1 September 2020; Published: June 2021
First available in Project Euclid: 9 August 2021

MathSciNet: MR4298879
zbMATH: 1475.62087
Digital Object Identifier: 10.1214/20-AOS2020

Subjects:
Primary: 62F03 , 62G10
Secondary: 62C07 , 62C15

Keywords: admissible decisions , Bayes factor , global null , Hypothesis testing , multiple hypothesis testing , test martingale

Rights: Copyright © 2021 Institute of Mathematical Statistics

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Vol.49 • No. 3 • June 2021
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