A note on e-values and multiple testing

Abstract

We discover a connection between the Benjamini–Hochberg procedure and the e -Benjamini–Hochberg procedure (Wang & Ramdas, 2022) with a suitably defined set of e -values. This insight extends to Storey’s procedure and generalized versions of the Benjamini–Hochberg procedure and the model-free multiple testing procedure of Barber & Candés (2015) with a general form of rejection rules. We further summarize these findings in a unified form. These connections open up new possibilities for designing multiple testing procedures in various contexts by aggregating e -values from different procedures or assembling e -values from different data subsets.