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A comprehensive error rate for multiple testing

Author

Listed:
  • Djalel-Eddine Meskaldji

    (École Polytechnique Fédérale de Lausanne (EPFL)
    École Polytechnique Fédérale de Lausanne (EPFL)
    École Polytechnique Fédérale de Lausanne (EPFL))

  • Dimitri Van De Ville

    (University of Geneva
    École Polytechnique Fédérale de Lausanne (EPFL))

  • Jean-Philippe Thiran

    (École Polytechnique Fédérale de Lausanne (EPFL))

  • Stephan Morgenthaler

    (École Polytechnique Fédérale de Lausanne (EPFL))

Abstract

Over the last two decades, a large variety of type I error rates and control procedures have been proposed in the field of multiple hypotheses testing. This paper proposes a framework that includes many existing proposals by investigating procedures in which the ordered p-values are compared to an arbitrary positive and non-decreasing threshold sequence. For this case, we derive the error rate being controlled under different assumptions on the p-values. Our focus will be on step-up procedures. The new formulation gives insight into the relations between existing error rates and opens new perspectives for the whole field of multiple testing.

Suggested Citation

  • Djalel-Eddine Meskaldji & Dimitri Van De Ville & Jean-Philippe Thiran & Stephan Morgenthaler, 2020. "A comprehensive error rate for multiple testing," Statistical Papers, Springer, vol. 61(5), pages 1859-1874, October.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:5:d:10.1007_s00362-018-1008-y
    DOI: 10.1007/s00362-018-1008-y
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    References listed on IDEAS

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    1. van der Laan Mark J. & Dudoit Sandrine & Pollard Katherine S., 2004. "Augmentation Procedures for Control of the Generalized Family-Wise Error Rate and Tail Probabilities for the Proportion of False Positives," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-27, June.
    2. Mark van der Laan & Sandrine Dudoit & Katherine Pollard, 2004. "Multiple Testing. Part III. Procedures for Control of the Generalized Family-Wise Error Rate and Proportion of False Positives," U.C. Berkeley Division of Biostatistics Working Paper Series 1140, Berkeley Electronic Press.
    3. Efron B. & Tibshirani R. & Storey J.D. & Tusher V., 2001. "Empirical Bayes Analysis of a Microarray Experiment," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1151-1160, December.
    4. Christopher Genovese & Larry Wasserman, 2002. "Operating characteristics and extensions of the false discovery rate procedure," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 499-517, August.
    5. Gudrun Bernhard & Markus Klein & Gerhard Hommel, 2004. "Global and multiple test procedures using ordered p-values—a review," Statistical Papers, Springer, vol. 45(1), pages 1-14, January.
    6. Christopher R. Genovese & Kathryn Roeder & Larry Wasserman, 2006. "False discovery control with p-value weighting," Biometrika, Biometrika Trust, vol. 93(3), pages 509-524, September.
    7. Yoav Benjamini, 2010. "Discovering the false discovery rate," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 405-416, September.
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