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Bounds on generalized family-wise error rates for normal distributions

Author

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  • Monitirtha Dey

    (Indian Statistical Institute)

  • Subir Kumar Bhandari

    (Indian Statistical Institute)

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.

Suggested Citation

  • Monitirtha Dey & Subir Kumar Bhandari, 2024. "Bounds on generalized family-wise error rates for normal distributions," Statistical Papers, Springer, vol. 65(4), pages 2313-2326, June.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:4:d:10.1007_s00362-023-01487-0
    DOI: 10.1007/s00362-023-01487-0
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