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More Powerful Control of the False Discovery Rate Under Dependence

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  • Alessio Farcomeni

Abstract

In a breakthrough paper, Benjamini and Hochberg (J Roy Stat Soc Ser B 57:289–300, 1995) proposed a new error measure for multiple testing, the FDR; and developed a distribution-free procedure to control it under independence among the test statistics. In this paper we argue by extensive simulation and theoretical considerations that the assumption of independence is not needed. Along the lines of (Ann Stat 32:1035–1061, 2004b), we moreover provide a more powerful method, that exploits an estimator of the number of false nulls among the tests. We propose a whole family of iterative estimators that prove robust under dependence and independence between the test statistics. These estimators can be used to improve also classical multiple testing procedures, and in general to estimate the weight of a known component in a mixture distribution. Innovations are illustrated by simulations.
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Suggested Citation

  • Alessio Farcomeni, 2006. "More Powerful Control of the False Discovery Rate Under Dependence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(1), pages 43-73, May.
    • Handle: RePEc:spr:stmapp:v:15:y:2006:i:1:p:43-73
    DOI: 10.1007/s10260-006-0002-z
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Edward Ip, 2001. "Testing for local dependency in dichotomous and polytomous item response models," Psychometrika, Springer;The Psychometric Society, vol. 66(1), pages 109-132, March.
    4. 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.
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    Cited by:

    1. A. Farcomeni & L. Finos, 2013. "FDR Control with Pseudo-Gatekeeping Based on a Possibly Data Driven Order of the Hypotheses," Biometrics, The International Biometric Society, vol. 69(3), pages 606-613, September.
    2. Farcomeni, Alessio & Pacillo, Simona, 2011. "A conservative estimator for the proportion of false nulls based on Dvoretzky, Kiefer and Wolfowitz inequality," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1867-1870.
    3. Dallakyan, Aramayis & Kim, Rakheon & Pourahmadi, Mohsen, 2022. "Time series graphical lasso and sparse VAR estimation," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).

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