Asymptotics in multiple hypotheses testing under dependence: beyond normality

Monitirtha Dey ()
Additional contact information
Monitirtha Dey: University of Bremen

Statistical Papers, 2025, vol. 66, issue 7, No 1, 14 pages

Abstract: Abstract This paper considers the classical simultaneous inference problem of testing several means in a general correlated framework. We establish an upper bound on the family-wise error rate(FWER) of Bonferroni’s procedure for equicorrelated test statistics (under general distributional assumptions). Consequently, we find that for a quite general class of distributions, Bonferroni FWER asymptotically tends to zero when the number of hypotheses approaches infinity. We extend this result to general positively correlated elliptically contoured setups. Then, we establish a general theorem which holds for the class of step-down procedures under a quite general class of elliptically contoured distributions, and a wide variety of correlation structures. The results obtained in this work generalize existing results for correlated Normal test statistics and facilitate new insights into the performances of multiple testing procedures under dependence.

Keywords: Familywise error rate; Multiple testing under dependence; Stepwise procedures; Holm’s method; Elliptically contoured distributions; 62J15; 62F03 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s00362-025-01770-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:stpapr:v:66:y:2025:i:7:d:10.1007_s00362-025-01770-2

Ordering information: This journal article can be ordered from
http://www.springer. ... business/journal/362

DOI: 10.1007/s00362-025-01770-2

Access Statistics for this article

Statistical Papers is currently edited by C. Müller, W. Krämer and W.G. Müller

More articles in Statistical Papers from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().