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Unimprovability of the Bonferroni procedure in the class of general step-up multiple testing procedures

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  • Gordon, Alexander Y.

Abstract

We introduce the class of general step-up multiple testing procedures (step-up MTPs), which contains the usually considered Benjamini-Hochberg type procedures (we call them threshold step-up MTPs) as a parametric subclass. We show that, under the natural condition of monotonicity, the Bonferroni procedure cannot be improved on, while controlling the family-wise error rate (FWER) at the same level, in the class of step-up procedures. This is in contrast to the class of step-down MTPs, where the Holm procedure is a classic example of such an improvement.

Suggested Citation

  • Gordon, Alexander Y., 2007. "Unimprovability of the Bonferroni procedure in the class of general step-up multiple testing procedures," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 117-122, January.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:2:p:117-122
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    Cited by:

    1. Gordon, Alexander Y., 2009. "Inequalities between generalized familywise error rates of a multiple testing procedure," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 1996-2004, October.
    2. Gordon, Alexander Y. & Salzman, Peter, 2008. "Optimality of the Holm procedure among general step-down multiple testing procedures," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1878-1884, September.
    3. Gordon, Alexander Y., 2012. "A sharp upper bound for the expected number of false rejections," Statistics & Probability Letters, Elsevier, vol. 82(8), pages 1507-1514.
    4. Gordon, Alexander Y., 2014. "Smoothing of stepwise multiple testing procedures," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 149-157.
    5. Georg Hahn, 2018. "Closure properties of classes of multiple testing procedures," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(2), pages 167-178, April.

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