Bounds on generalized family-wise error rates for normal distributions
Article Type
Research Article
Publication Title
Statistical Papers
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.
First Page
2313
Last Page
2326
DOI
10.1007/s00362-023-01487-0
Publication Date
6-1-2024
Recommended Citation
Dey, Monitirtha and Bhandari, Subir Kumar, "Bounds on generalized family-wise error rates for normal distributions" (2024). Journal Articles. 4630.
https://digitalcommons.isical.ac.in/journal-articles/4630