B1806
Title: Online multiple testing with super uniformity reward
Authors: Sebastian Doehler - Darmstadt University of Applied Science (Germany) [presenting]
Etienne Roquain - University Pierre et Marie Curie (France)
Iqraa Meah - Universite Sorbonne and Darmstadt University of Applied Science (Germany)
Abstract: Online multiple testing refers to the setting where a possibly infinite number of hypotheses are tested, and the p-values are available one by one sequentially. This differs from classical multiple testing where the number of tested hypotheses is finite and known beforehand, and the p-values are available simultaneously. It is well-known that the existing methods for online multiple testing can suffer from a significant loss of power if the null p-values are conservative. The previously introduced methodology is extended to obtain more powerful procedures for the case of super-uniformly distributed p-values. These types of p-values arise in important settings, e.g. when discrete hypothesis tests are performed or when the p-values are weighted. To this end, the method of superuniformity reward (SUR) is introduced that incorporates information about the individual null cumulative distribution functions. The approach yields several new rewarded procedures that offer uniform power improvements over known procedures and come with mathematical guarantees for controlling online error criteria based either on the family-wise error rate (FWER) or the marginal false discovery rate (mFDR).
