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Generalized Augmentation to Control the False Discovery Exceedance in Multiple Testing

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  • ALESSIO FARCOMENI

Abstract

A new multiple testing procedure, the generalized augmentation procedure (GAUGE), is introduced. The procedure is shown to control the false discovery exceedance and to be competitive in terms of power. It is also shown how to apply the idea of GAUGE to achieve control of other error measures. Extensions to dependence are discussed, together with a modification valid under arbitrary dependence. We present an application to an original study on prostate cancer and on a benchmark data set on colon cancer. Copyright (c) 2009 Board of the Foundation of the Scandinavian Journal of Statistics.

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  • Alessio Farcomeni, 2009. "Generalized Augmentation to Control the False Discovery Exceedance in Multiple Testing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 501-517.
  • Handle: RePEc:bla:scjsta:v:36:y:2009:i:3:p:501-517
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    References listed on IDEAS

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    1. Yoav Benjamini & Abba M. Krieger & Daniel Yekutieli, 2006. "Adaptive linear step-up procedures that control the false discovery rate," Biometrika, Biometrika Trust, vol. 93(3), pages 491-507, September.
    2. Art B. Owen, 2005. "Variance of the number of false discoveries," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 411-426.
    3. 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.
    4. van der Laan Mark J. & Dudoit Sandrine & Pollard Katherine S., 2004. "Multiple Testing. Part II. Step-Down Procedures for Control of the Family-Wise Error Rate," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-35, June.
    5. Yoav Benjamini & Yosef Hochberg, 2000. "On the Adaptive Control of the False Discovery Rate in Multiple Testing With Independent Statistics," Journal of Educational and Behavioral Statistics, , vol. 25(1), pages 60-83, March.
    6. Guo Wenge & Romano Joseph, 2007. "A Generalized Sidak-Holm Procedure and Control of Generalized Error Rates under Independence," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 6(1), pages 1-35, January.
    7. Mark van der Laan & Sandrine Dudoit & Katherine Pollard, 2004. "Multiple Testing. Part II. Step-Down Procedures for Control of the Family-Wise Error Rate," U.C. Berkeley Division of Biostatistics Working Paper Series 1138, Berkeley Electronic Press.
    8. M. Perone Pacifico & C. Genovese & I. Verdinelli & L. Wasserman, 2004. "False Discovery Control for Random Fields," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1002-1014, December.
    9. Alessio Farcomeni, 2007. "Some Results on the Control of the False Discovery Rate under Dependence," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(2), pages 275-297.
    10. Genovese, Christopher R. & Wasserman, Larry, 2006. "Exceedance Control of the False Discovery Proportion," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1408-1417, December.
    11. van der Laan Mark J. & Birkner Merrill D. & Hubbard Alan E., 2005. "Empirical Bayes and Resampling Based Multiple Testing Procedure Controlling Tail Probability of the Proportion of False Positives," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, October.
    12. 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.
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    Cited by:

    1. Axel Gandy & Georg Hahn, 2014. "MMCTest—A Safe Algorithm for Implementing Multiple Monte Carlo Tests," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1083-1101, December.
    2. Cerioli, Andrea & Farcomeni, Alessio, 2011. "Error rates for multivariate outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 544-553, January.
    3. Thorsten Dickhaus, 2012. "Simultaneous Statistical Inference in Dynamic Factor Models," SFB 649 Discussion Papers SFB649DP2012-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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