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The false discovery rate (FDR) of multiple tests in a class room lecture

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  • Benditkis, Julia
  • Heesen, Philipp
  • Janssen, Arnold

Abstract

Multiple tests are designed to test a whole collection of null hypotheses simultaneously. Their quality is often judged by the false discovery rate (FDR), i.e. the expectation of the quotient of the number of false rejections divided by the number of all rejections. The widely cited Benjamini and Hochberg (BH) step up multiple test controls the FDR under various regularity assumptions. In this note we present a rapid approach to the BH step up and step down tests. Also, sharp FDR inequalities are discussed for dependent p-values and examples and counter-examples are considered. In particular, the Bonferroni bound is sharp under dependence for the control of the family-wise error rate.

Suggested Citation

  • Benditkis, Julia & Heesen, Philipp & Janssen, Arnold, 2018. "The false discovery rate (FDR) of multiple tests in a class room lecture," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 29-35.
    • Handle: RePEc:eee:stapro:v:134:y:2018:i:c:p:29-35
    DOI: 10.1016/j.spl.2017.09.017
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    References listed on IDEAS

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    1. Guo, Wenge & Bhaskara Rao, M., 2008. "On optimality of the Benjamini-Hochberg procedure for the false discovery rate," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2024-2030, October.
    2. John D. Storey, 2002. "A direct approach to false discovery rates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 479-498, August.
    3. John D. Storey & Jonathan E. Taylor & David Siegmund, 2004. "Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: a unified approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 187-205, February.
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    Cited by:

    1. Izmirlian, Grant, 2020. "Strong consistency and asymptotic normality for quantities related to the Benjamini–Hochberg false discovery rate procedure," Statistics & Probability Letters, Elsevier, vol. 160(C).

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