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A multivariate version of the Benjamini-Hochberg method

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  • Ferreira, J.A.
  • Nyangoma, S.O.

Abstract

We propose a multivariate method for combining results from independent studies about the same 'large scale' multiple testing problem. The method works asymptotically in the number of hypotheses and consists of applying the Benjamini-Hochberg procedure to the p-values of each study separately by determining the 'individual false discovery rates' which maximize power subject to a restriction on the (global) false discovery rate. We show how to obtain solutions to the associated optimization problem, provide both theoretical and numerical examples, and compare the method with univariate ones.

Suggested Citation

  • Ferreira, J.A. & Nyangoma, S.O., 2008. "A multivariate version of the Benjamini-Hochberg method," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2108-2124, October.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:9:p:2108-2124
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    References listed on IDEAS

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    1. Ferreira José António & Zwinderman Aeilko H, 2006. "Approximate Power and Sample Size Calculations with the Benjamini-Hochberg Method," The International Journal of Biostatistics, De Gruyter, vol. 2(1), pages 1-38, September.
    2. Allison, David B. & Gadbury, Gary L. & Heo, Moonseong & Fernandez, Jose R. & Lee, Cheol-Koo & Prolla, Tomas A. & Weindruch, Richard, 2002. "A mixture model approach for the analysis of microarray gene expression data," Computational Statistics & Data Analysis, Elsevier, vol. 39(1), pages 1-20, March.
    3. Mette Langaas & Bo Henry Lindqvist & Egil Ferkingstad, 2005. "Estimating the proportion of true null hypotheses, with application to DNA microarray data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(4), pages 555-572, September.
    4. Xiang, Qinfang & Edwards, Jode & Gadbury, Gary L., 2006. "Interval estimation in a finite mixture model: Modeling P-values in multiple testing applications," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 570-586, November.
    5. Christopher Genovese & Larry Wasserman, 2002. "Operating characteristics and extensions of the false discovery rate procedure," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 499-517, August.
    6. 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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