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Balanced Control of Generalized Error Rates

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  • Joseph P. Romano
  • Michael Wolf

Abstract

Consider the problem of testing s hypotheses simultaneously. In this paper, we derive methods which control the generalized familywise error rate given by the probability of k or more false rejections, abbreviated k-FWER. We derive both single-step and stepdown procedures that control the k-FWER in finite samples or asymptotically, depending on the situation. Moreover, the procedures are asymptotically balanced in an appropriate sense. We briefly consider control of the average number of false rejections. Additionally, we consider the false discovery proportion (FDP), defined as the number of false rejections divided by the total number of rejections (and defined to be 0 if there are no rejections). Here, the goal is to construct methods which satisfy, for given g and a, P{FDP > g}

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Bibliographic Info

Paper provided by Institute for Empirical Research in Economics - University of Zurich in its series IEW - Working Papers with number 379.

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Date of creation: Jul 2008
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Handle: RePEc:zur:iewwpx:379

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Keywords: Bootstrap; False Discovery Proportion; Generalized familywise error rate; Multiple Testing; Stepdown procedure;

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References

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  1. Joseph P. Romano & Michael Wolf, 2005. "Exact and Approximate Stepdown Methods for Multiple Hypothesis Testing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 94-108, March.
  2. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2008. "Control of the False Discovery Rate under Dependence using the Bootstrap and Subsampling," IEW - Working Papers 337, Institute for Empirical Research in Economics - University of Zurich.
  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. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2010. "multiple testing," The New Palgrave Dictionary of Economics, Palgrave Macmillan.
  5. 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.
  6. 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.
  7. 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.
  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. Dudoit Sandrine & van der Laan Mark J. & Pollard Katherine S., 2004. "Multiple Testing. Part I. Single-Step Procedures for Control of General Type I Error Rates," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-71, June.
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Cited by:
  1. Christopher J. Bennett, 2009. "p-Value Adjustments for Asymptotic Control of the Generalized Familywise Error Rate," Vanderbilt University Department of Economics Working Papers 0905, Vanderbilt University Department of Economics.

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