FWER Goes to Zero for Correlated Normal

2021/10/11 by Monitirtha Dey, Dey, Monitirtha, Subir Kumar Bhandari +1 · 2 citations
Mathematics · #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.2110.05070

8 pages; typos corrected, references added. Earlier results extended to arbitrarily correlated setups

arxiv created 2021/12/06 · arxiv updated 2021/12/07

Abstract

Familywise error rate (FWER) has been a cornerstone in simultaneous inference for decades, and the classical Bonferroni method has been one of the most prominent frequentist approaches for controlling FWER. The present article studies the limiting behavior of Bonferroni FWER in a multiple testing problem as the number of hypotheses grows to infinity. We establish that in the equicorrelated normal setup with positive equicorrelation, Bonferroni FWER tends to zero asymptotically. We extend this result for generalized familywise error rates and to arbitrarily correlated setups.

Cited by

• An asymptotically exact multiple testing procedure under dependence
• Some Results on Generalized Familywise Error Rate Controlling Procedures under Dependence

Related

• Behaviour of FWER in Normal Distributions
• Bound on FWER for correlated normal distribution
• On Asymptotic Behaviors of Stepwise Multiple Testing Procedures
• Asymptotics in Multiple Hypotheses Testing under Dependence: beyond Normality
• Observation on F.W.E.R. and F.D.R. for correlated normal