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
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
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