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The optimal power puzzle: scrutiny of the monotone likelihood ratio assumption in multiple testing

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  • Hongyuan Cao
  • Wenguang Sun
  • Michael R. Kosorok

Abstract

In single hypothesis testing, power is a nondecreasing function of Type I error rate; hence it is desirable to test at the nominal level exactly to achieve optimal power. The optimal power puzzle arises from the fact that for multiple testing under the false discovery rate paradigm, such a monotonic relationship may not hold. In particular, exact false discovery rate control may lead to a less powerful testing procedure if a test statistic fails to fulfil the monotone likelihood ratio condition. In this article, we identify different scenarios wherein the condition fails and give caveats for conducting multiple testing in practical settings. Copyright 2013, Oxford University Press.

Suggested Citation

  • Hongyuan Cao & Wenguang Sun & Michael R. Kosorok, 2013. "The optimal power puzzle: scrutiny of the monotone likelihood ratio assumption in multiple testing," Biometrika, Biometrika Trust, vol. 100(2), pages 495-502.
    • Handle: RePEc:oup:biomet:v:100:y:2013:i:2:p:495-502
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    File URL: http://hdl.handle.net/10.1093/biomet/ast001
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    Cited by:

    1. Joungyoun Kim & Donghyeon Yu & Johan Lim & Joong-Ho Won, 2018. "A peeling algorithm for multiple testing on a random field," Computational Statistics, Springer, vol. 33(1), pages 503-525, March.
    2. Jiaying Gu & Roger Koenker, 2023. "Invidious Comparisons: Ranking and Selection as Compound Decisions," Econometrica, Econometric Society, vol. 91(1), pages 1-41, January.
    3. Jiaying Gu & Roger Koenker, 2016. "On a Problem of Robbins," International Statistical Review, International Statistical Institute, vol. 84(2), pages 224-244, August.
    4. Zhigen Zhao, 2022. "Where to find needles in a haystack?," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 148-174, March.
    5. T. Tony Cai & Wenguang Sun & Weinan Wang, 2019. "Covariate‐assisted ranking and screening for large‐scale two‐sample inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 187-234, April.
    6. Jiaying Gu & Roger Koenker, 2020. "Invidious Comparisons: Ranking and Selection as Compound Decisions," Papers 2012.12550, arXiv.org, revised Sep 2021.

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