Behaviour of Familywise Error Rate in Normal Distributions
Abstract
We study the behaviour of the familywise error rate (FWER) for Bonferronitype 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 $\rho$ and hence an upper bound on the FWER of Bonferroni$\alpha$ procedure is given by $\alpha(1  \rho)$. We derive upper bounds on FWER for Bonferroni method under the equicorrelated and general normal setups in asymptotic and nonasymptotic case. We show similar results for generalized familywise error rates.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2107.00146
 Bibcode:
 2021arXiv210700146D
 Keywords:

 Mathematics  Statistics Theory;
 Mathematics  Probability
 EPrint:
 25 pages, 2 figures