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A Method to Increase the Power of Multiple Testing Procedures Through Sample Splitting

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Author Info

  • Rubin Daniel

    (University of California, Berkeley)

  • Dudoit Sandrine

    (University of California, Berkeley)

  • van der Laan Mark

    (University of California, Berkeley)

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    Abstract

    Consider the standard multiple testing problem where many hypotheses are to be tested, each hypothesis is associated with a test statistic, and large test statistics provide evidence against the null hypotheses. One proposal to provide probabilistic control of Type-I errors is the use of procedures ensuring that the expected number of false positives does not exceed a user-supplied threshold. Among such multiple testing procedures, we derive the most powerful method, meaning the test statistic cutoffs that maximize the expected number of true positives. Unfortunately, these optimal cutoffs depend on the true unknown data generating distribution, so could never be used in a practical setting. We instead consider splitting the sample so that the optimal cutoffs are estimated from a portion of the data, and then testing on the remaining data using these estimated cutoffs. When the null distributions for all test statistics are the same, the obvious way to control the expected number of false positives would be to use a common cutoff for all tests. In this work, we consider the common cutoff method as a benchmark multiple testing procedure. We show that in certain circumstances the use of estimated optimal cutoffs via sample splitting can dramatically outperform this benchmark method, resulting in increased true discoveries, while retaining Type-I error control. This paper is an updated version of the work presented in Rubin et al. (2005), later expanded upon by Wasserman and Roeder (2006).

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    File URL: http://www.degruyter.com/view/j/sagmb.2006.5.1/sagmb.2006.5.1.1148/sagmb.2006.5.1.1148.xml?format=INT
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    Bibliographic Info

    Article provided by De Gruyter in its journal Statistical Applications in Genetics and Molecular Biology.

    Volume (Year): 5 (2006)
    Issue (Month): 1 (August)
    Pages: 1-20

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    Handle: RePEc:bpj:sagmbi:v:5:y:2006:i:1:n:19

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    Web page: http://www.degruyter.com

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    Web: http://www.degruyter.com/view/j/sagmb

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    Cited by:
    1. Miecznikowski, Jeffrey C. & Gold, David & Shepherd, Lori & Liu, Song, 2011. "Deriving and comparing the distribution for the number of false positives in single step methods to control k-FWER," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1695-1705, November.
    2. Òscar Jordà & Malte Knüppel & Massimiliano Marcellino, 2010. "Empirical Simultaneous Confidence Regions for Path-Forecasts," Economics Working Papers ECO2010/18, European University Institute.
    3. Habiger, Joshua D. & Peña, Edsel A., 2014. "Compound p-value statistics for multiple testing procedures," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 153-166.

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