FDR- and FWE-controlling methods using data-driven weights

Weighted methods are an important feature of multiplicity control methods. The weights must usually be chosen a priori, on the basis of experimental hypotheses. Under some conditions, however, they can be chosen making use of information from the data (therefore a posteriori) while maintaining multiplicity control. In this paper we provide: (1) a review of weighted methods for familywise type I error rate (FWE) (both parametric and nonparametric) and false discovery rate (FDR) control; (2) a review of data-driven weighted methods for FWE control; (3) a new proposal for weighted FDR control (data-driven weights) under independence among variables; (4) under any type of dependence; (5) a simulation study that assesses the performance of procedure of point 4 under various conditions.