TY - JOUR
T1 - Adaptive controls of FWER and FDR under block dependence
AU - Guo, Wenge
AU - Sarkar, Sanat
N1 - Funding Information:
The research of the first author is supported by the NSF Grants DMS-1006021 , DMS-1309162 and the research of the second author is supported by the NSF Grant DMS-1006344 , DMS-1309273 .
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2020/9
Y1 - 2020/9
N2 - 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.
AB - 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.
KW - Adaptive Benjamini–Hochberg method
KW - Adaptive Bonferroni method
KW - False discovery rate
KW - Familywise error rate
KW - Multiple testing
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U2 - 10.1016/j.jspi.2018.03.008
DO - 10.1016/j.jspi.2018.03.008
M3 - Article
AN - SCOPUS:85079288947
SN - 0378-3758
VL - 208
SP - 13
EP - 24
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
ER -