Bounds on generalized family-wise error rates for normal distributions

Monitirtha Dey () and Subir Kumar Bhandari ()
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Monitirtha Dey: Indian Statistical Institute
Subir Kumar Bhandari: Indian Statistical Institute

Statistical Papers, 2024, vol. 65, issue 4, No 16, 2313-2326

Abstract: Abstract The Bonferroni procedure has been one of the foremost frequentist approaches for controlling the family-wise error rate (FWER) in simultaneous inference. However, many scientific disciplines often require less stringent error rates. One such measure is the generalized family-wise error rate (gFWER) proposed (Lehmann and Romano in Ann Stat 33(3):1138–1154, 2005, https://doi.org/10.1214/009053605000000084 ). FWER or gFWER controlling methods are considered highly conservative in problems with a moderately large number of hypotheses. Although, the existing literature lacks a theory on the extent of the conservativeness of gFWER controlling procedures under dependent frameworks. In this note, we address this gap in a unified manner by establishing upper bounds for the gFWER under arbitrarily correlated multivariate normal setups with moderate dimensions. Towards this, we derive a new probability inequality which, in turn, extends and sharpens a classical inequality. Our results also generalize a recent related work by the first author.

Keywords: Generalized family-wise error rate; k-FWER; Lehmann–Romano method; Multiple testing under dependence; 62J15; 62F03 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01487-0

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