Behaviour of Familywise Error Rate in Normal Distributions
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We study the behaviour of the familywise error rate (FWER) for Bonferroni-type procedure in multiple testing problem. Das and Bhandari in a recent article have shown that, in the equicorrelated normal setup, FWER asymptotically (i.e when number of hypotheses is very large) is a convex function of correlation ρ and hence an upper bound on the FWER of Bonferroni-α procedure is given by α(1 - ρ). We derive upper bounds on FWER for Bonferroni method under the equicorrelated and general normal setups in asymptotic and non-asymptotic case. We show similar results for generalized familywise error rates.
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