Bonferroni-type Plug-in Procedure Controlling Generalized Familywise Error Rate

Abstract

Consider the multiple hypotheses testing problem controlling the generalized familywise error rate k-FWER, the probability of at least k false rejections. We propose a plug-in procedure based on the estimation of the number of true null hypotheses. Under the independence assumption of the p-values corresponding to the true null hypotheses, we first introduce the least favorable configuration (LFC) of k-FWER for Bonferroni-type plug-in procedure, then we construct a plug-in k-FWER-controlled procedure based on LFC. For dependent p-values, we establish the asymptotic k-FWER control under some mild conditions. Simulation studies suggest great improvement over generalized Bonferroni test and generalized Holm test.

Keywords:

• Generalized Bonferroni procedure
• Generalized familywise error rate
• Multiple hypotheses testing
• Plug-in estimate

Mathematics Subject Classification:

• Primary 62H15
• Secondary 62H99