E-values: Calibration, combination and applications
The Annals of Statistics · 2021 · Volume 49 · Issue 3
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.
Keywords
62C07, 62C15, 62F03, 62G10, admissible decisions, Bayes factor, global null, Hypothesis testing, multiple hypothesis testing, test martingale
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