Adaptive controls of FWER and FDR under block dependence

Wenge Guo, Sanat Sarkar

Research output: Contribution to journalArticle

Abstract

Often in multiple testing, the hypotheses appear in non-overlapping blocks with the associated p-values exhibiting dependence within but not between blocks. We consider adapting the Benjamini–Hochberg method for controlling the false discovery rate (FDR) and the Bonferroni method for controlling the familywise error rate (FWER) to such dependence structure without losing their ultimate controls over the FDR and FWER, respectively, in a non-asymptotic setting. We present variants of conventional adaptive Benjamini–Hochberg and Bonferroni methods with proofs of their respective controls over the FDR and FWER. Numerical evidence is presented to show that these new adaptive methods can capture the present dependence structure more effectively than the corresponding conventional adaptive methods. This paper offers a solution to the open problem of constructing adaptive FDR and FWER controlling methods under dependence in a non-asymptotic setting and providing real improvements over the corresponding non-adaptive ones.

Original languageEnglish (US)
Pages (from-to)13-24
Number of pages12
JournalJournal of Statistical Planning and Inference
Volume208
DOIs
StateAccepted/In press - Jan 1 2020

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Adaptive Benjamini–Hochberg method
  • Adaptive Bonferroni method
  • False discovery rate
  • Familywise error rate
  • Multiple testing

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