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A sharp upper bound for the expected number of false rejections

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  • Gordon, Alexander Y.
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    Abstract

    We consider the class of monotone multiple testing procedures (monotone MTPs). It includes, among others, traditional step-down (Holm type) and step-up (Benjamini–Hochberg type) MTPs, as well as their generalization–step-up-down procedures (Tamhane et al., 1998). Our main result–the All-or-Nothing Theorem–allows us to explicitly calculate, for each MTP in those classes, its per-family error rate–the exact level at which the procedure controls the expected number of false rejections under general and unknown dependence structure of the individual tests. As an illustration, we show that, for any monotone step-down procedure (where the term “step-down” is understood in the most general sense), the ratio of its per-family error rate and its familywise error rate (the exact level at which the procedure controls the probability of one or more false rejections) does not exceed 4 if the denominator is less than 1.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 8 ()
    Pages: 1507-1514

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:8:p:1507-1514

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    Keywords: Multiple testing procedure; Monotone procedure; Per-family error rate; Step-down procedure; Step-up procedure;

    References

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    1. 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.
    2. 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.
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    Cited by:
    1. Gordon, Alexander Y., 2014. "Smoothing of stepwise multiple testing procedures," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 149-157.

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