Confidence and discoveries with e-values

Abstract: We discuss systematically two versions of confidence regions: those based on p-values and those based on e-values, a recent alternative to p-values. Both versions can be applied to multiple hypothesis testing, and in this paper we are interested in procedures that control the number of false discoveries under arbitrary dependence between the base p- or e-values. We introduce a procedure that is based on e-values and show that it is efficient both computationally and statistically using simulated and real-world datasets. Comparison with the corresponding standard procedure based on p-values is not straightforward, but there are indications that the new one performs significantly better in some situations.