Adaptive procedure for generalized familywise error rate control

ABSTRACT

This article considers multiple hypotheses testing with the generalized familywise error rate k-FWER control, which is the probability of at least k false rejections. We first assume the p-values corresponding to the true null hypotheses are independent, and propose adaptive generalized Bonferroni procedure with k-FWER control based on the estimation of the number of true null hypotheses. Then, we assume the p-values are dependent, satisfying block dependence, and propose adaptive procedure with k-FWER control. Extensive simulations compare the performance of the adaptive procedures with different estimators.

KEYWORDS:

• Adaptive procedure
• Generalized Bonferroni procedure
• Generalized familywise error rate
• Multiple hypotheses testing

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62H15
• Secondary 62H99

Acknowledgments

The author would like to thank the editor and the referee for their useful comments, which led to considerable improvement of the article. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11471035, 11626227 and 11671398) and the Fundamental Research Funds for the Central Universities (Grant No. 2015QS03).