E-values: Calibration, combination, and applications

Vladimir Vovk, Ruodu Wang

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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.
Original languageEnglish
Pages (from-to)1736-1754
Number of pages19
JournalThe Annals of Statistics
Issue number3
Publication statusPublished - 9 Aug 2021


  • hypothesis testing
  • multiple hypothesis testing
  • global null
  • admissible decisions
  • test martingale
  • Bayes factor

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