Generalized FWER control procedures for testing multiple hypotheses

Abstract

Most methods for testing multiple hypotheses assume the monotone likelihood ratio (MLR) condition holds. In fact, in some cases, MLR does not hold, and the widely used Bonferroni procedure may be inefficient. In this paper, we aim to improve the Bonferroni procedure without assuming the MLR condition holds. By combining the advantages of the test method constructed according to the Neyman–Pearson lemma and the Bonferroni procedure, we propose two generalized Bonferroni procedures, denoted as GB1 and GB2. Further, we propose to plug the proportion of true null hypotheses in the GB2 procedure to improve power. We numerically compare the proposed methods with existing methods. Simulation results show that the proposed methods perform very close to or significantly better than existing ones; the proposed plug-in procedure performs best among all in terms of power performance. Two real data sets are analyzed with the proposed procedures.

Keywords:

• Monotone likelihood ratio condition
• Bonferroni procedure
• FWER
• Multiple hypotheses

Additional information

Funding

Haibing Zhao’s work was supported by a grant from the National Natural Science Foundation of China (NSFC) [No.11471204].