Séance Séminaire

Séminaire de Probabilités et Statistique

Online multiple testing with super-uniformity reward

Online multiple testing refers to the context where a possibly infinite number of hypotheses are tested, and the $p$-values are available one by one sequentially. This context differs from the usual one where the number of hypotheses to test $m < \infty$ is known beforehand, and the $p$-values are available together. The online methods proposed so far can suffer from a significant loss of power when the $p$-values are obtained from discrete tests. To resolve this issue, we introduce the method of super-uniformity reward that incorporates information about the individual null cumulative distribution functions. We prove that the rewarded procedures uniformly improve upon the non-rewarded ones while keeping the type I error control, and illustrate their performance on simulated and real data application.