E-values: Calibration, combination, and applications

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.

48 pages, 5 figures, 4 algorithms. A new title and improved presentation

References in corpus (2)

• Universal Inference
• Interactive Martingale Tests for the Global Null

Cited by in corpus (12)

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• False discovery rate control with e-values
• ALL-IN meta-analysis: breathing life into living systematic reviews and prospective meta-analyses
• Comment on Glenn Shafer's "Testing by betting"
• Inference for Large Panel Data with Many Covariates
• Superconsistency of Tests in High Dimensions
• Testing exchangeability: fork-convexity, supermartingales, and e-processes