Adaptive controls of FWER and FDR under block dependence

Document Type

Article

Publication Date

9-1-2020

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.

Identifier

85079288947 (Scopus)

Publication Title

Journal of Statistical Planning and Inference

External Full Text Location

https://doi.org/10.1016/j.jspi.2018.03.008

ISSN

03783758

First Page

13

Last Page

24

Volume

208

Grant

DMS-1309162

Fund Ref

National Science Foundation

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