TY - JOUR
T1 - Is Bonferroni Admissible for Large m?
AU - Lu, Yonggang
AU - Westfall, Peter H.
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2009
Y1 - 2009
N2 - Modern methods of multiple comparisons, particularly those based on controlling the false discovery rate, are lax relative to the Bonferroni method in their assignment of significances; they are relatively more lax as m, the number of tests, increases. We point out that this laxness is based on an assumption concerning the size of the loss due to Type I errors relative to the loss due to Type II errors, and challenge the generality of this assumption, providing an alternative loss function for which the Bonferroni method is asymptotically (as m → ∞) optimal.
AB - Modern methods of multiple comparisons, particularly those based on controlling the false discovery rate, are lax relative to the Bonferroni method in their assignment of significances; they are relatively more lax as m, the number of tests, increases. We point out that this laxness is based on an assumption concerning the size of the loss due to Type I errors relative to the loss due to Type II errors, and challenge the generality of this assumption, providing an alternative loss function for which the Bonferroni method is asymptotically (as m → ∞) optimal.
KW - Asymptotic theory
KW - Decision theory
KW - Extreme value theory
KW - Loss function
KW - Multiple comparisons
UR - http://www.scopus.com/inward/record.url?scp=76749139864&partnerID=8YFLogxK
U2 - 10.1080/01966324.2009.10737749
DO - 10.1080/01966324.2009.10737749
M3 - Article
AN - SCOPUS:76749139864
VL - 29
SP - 51
EP - 69
JO - American Journal of Mathematical and Management Sciences
JF - American Journal of Mathematical and Management Sciences
SN - 0196-6324
IS - 1-2
ER -