False discovery rate control with e‐values

By Ruodu Wang, Aaditya Ramdas. Journal of The Royal Statistical Society Series B-statistical Methodology, 2020

174 citations recorded by the source corpus.

E‐values have gained attention as potential alternatives to p‐values as measures of uncertainty, significance and evidence. In brief, e‐values are realized by random variables with expectation at most one under the null; examples include betting scores, (point null) Bayes factors, likelihood ratios and stopped supermartingales. We design a natural analogue of the Benjamini‐Hochberg (BH) procedure for false discovery rate (FDR) control that utilizes e‐values, called the e‐BH procedure, and compare it with the standard procedure for p‐values. One of our central results is that, unlike the usual BH procedure, the e‐BH procedure controls the FDR at the desired level—with no correction—for any dependence structure between the e‐values. We illustrate that the new procedure is convenient in various settings of complicated dependence, structured and post‐selection hypotheses, and multi‐armed bandit problems. Moreover, the BH procedure is a special case of the e‐BH procedure through calibration between p‐values and e‐values. Overall, the e‐BH procedure is a novel, powerful and general tool for multiple testing under dependence, that is complementary to the BH procedure, each being an appropriate choice in different applications.

Subfields: General Decision Sciences, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1053eea8449e0fcef4f06a36f6420d2b43406b1e

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Citations in the corpus

Time-uniform central limit theory and asymptotic confidence sequences (2021, background): “Nevertheless, working with the e-value Eτ directly makes it simple to combine evidence across several studies [12, 45, 56] or to control the false discovery rate under arbitrary dependence [58], both of which are less straightforward with p-values.”
Safe Testing (2019, background): “Although the concept is much older (Section 7), the interest in e -values and the related test martingales has exploded over the last three years (Wang and Ramdas, 2020; Vovk and Wang, 2021; Shafer, 2021; Henzi and Ziegel, 2022; Waudby-Smith and Ramdas, 2021; Orabona and Jun, 2021).”