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Adaptive linear step-up procedures that control the false discovery rate

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  • Yoav Benjamini
  • Abba M. Krieger
  • Daniel Yekutieli
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    Abstract

    The linear step-up multiple testing procedure controls the false discovery rate at the desired level q for independent and positively dependent test statistics. When all null hypotheses are true, and the test statistics are independent and continuous, the bound is sharp. When some of the null hypotheses are not true, the procedure is conservative by a factor which is the proportion m-sub-0/m of the true null hypotheses among the hypotheses. We provide a new two-stage procedure in which the linear step-up procedure is used in stage one to estimate m-sub-0, providing a new level q′ which is used in the linear step-up procedure in the second stage. We prove that a general form of the two-stage procedure controls the false discovery rate at the desired level q. This framework enables us to study analytically the properties of other procedures that exist in the literature. A simulation study is presented that shows that two-stage adaptive procedures improve in power over the original procedure, mainly because they provide tighter control of the false discovery rate. We further study the performance of the current suggestions, some variations of the procedures, and previous suggestions, in the case where the test statistics are positively dependent, a case for which the original procedure controls the false discovery rate. In the setting studied here the newly proposed two-stage procedure is the only one that controls the false discovery rate. The procedures are illustrated with two examples of biological importance. Copyright 2006, Oxford University Press.

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    Bibliographic Info

    Article provided by Biometrika Trust in its journal Biometrika.

    Volume (Year): 93 (2006)
    Issue (Month): 3 (September)
    Pages: 491-507

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    Handle: RePEc:oup:biomet:v:93:y:2006:i:3:p:491-507

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    Cited by:
    1. Brian Jacob & Max Kapustin & Jens Ludwig, 2014. "Human Capital Effects of Anti-Poverty Programs: Evidence from a Randomized Housing Voucher Lottery," NBER Working Papers 20164, National Bureau of Economic Research, Inc.
    2. Delattre, S. & Roquain, E., 2011. "On the false discovery proportion convergence under Gaussian equi-correlation," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 111-115, January.
    3. Michael L. Anderson, 2012. "The Benefits of College Athletic Success: An Application of the Propensity Score Design with Instrumental Variables," NBER Working Papers 18196, National Bureau of Economic Research, Inc.
    4. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2010. "Hypothesis Testing in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 75-104, 09.
    5. Daniel Yekutieli, 2008. "Comments on: Control of the false discovery rate under dependence using the bootstrap and subsampling," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 17(3), pages 458-460, November.
    6. Carlsson, Magnus & Eriksson, Stefan, 2014. "Discrimination in the rental market for apartments," Journal of Housing Economics, Elsevier, vol. 23(C), pages 41-54.
    7. Sara Heller & Harold A. Pollack & Roseanna Ander & Jens Ludwig, 2013. "Preventing Youth Violence and Dropout: A Randomized Field Experiment," NBER Working Papers 19014, National Bureau of Economic Research, Inc.
    8. 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.
    9. Kim, Donggyu & Zhang, Chunming, 2014. "Adaptive linear step-up multiple testing procedure with the bias-reduced estimator," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 31-39.
    10. Hanck, Christoph, 2011. "Now, whose schools are really better (or weaker) than Germany's? A multiple testing approach," Economic Modelling, Elsevier, vol. 28(4), pages 1739-1746, July.
    11. Jules Ellis, 2014. "An Inequality for Correlations in Unidimensional Monotone Latent Variable Models for Binary Variables," Psychometrika, Springer, vol. 79(2), pages 303-316, April.
    12. Joseph Romano & Azeem Shaikh & Michael Wolf, 2008. "Control of the false discovery rate under dependence using the bootstrap and subsampling," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 17(3), pages 417-442, November.
    13. Ding, Weili & Lehrer, Steven F., 2011. "Experimental Estimates of the Impacts of Class Size on Test Scores: Robustness and Heterogeneity," CLSSRN working papers clsrn_admin-2011-12, Vancouver School of Economics, revised 26 Jun 2011.
    14. 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.
    15. Philip J. Cook & Kenneth Dodge & George Farkas & Roland G. Fryer, Jr & Jonathan Guryan & Jens Ludwig & Susan Mayer & Harold Pollack & Laurence Steinberg, 2014. "The (Surprising) Efficacy of Academic and Behavioral Intervention with Disadvantaged Youth: Results from a Randomized Experiment in Chicago," NBER Working Papers 19862, National Bureau of Economic Research, Inc.
    16. Joseph P. Romano & Michael Wolf, 2008. "Balanced Control of Generalized Error Rates," IEW - Working Papers 379, Institute for Empirical Research in Economics - University of Zurich.
    17. Deckers, Thomas & Hanck, Christoph, 2009. "Multiple Testing Techniques in Growth Econometrics," MPRA Paper 17843, University Library of Munich, Germany.
    18. Cheng, Cheng, 2009. "Internal validation inferences of significant genomic features in genome-wide screening," Computational Statistics & Data Analysis, Elsevier, vol. 53(3), pages 788-800, January.
    19. Nik Tuzov & Frederi Viens, 2011. "Mutual fund performance: false discoveries, bias, and power," Annals of Finance, Springer, vol. 7(2), pages 137-169, May.
    20. repec:esm:wpaper:esmt-13-02 is not listed on IDEAS

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