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Classes of multiple decision functions strongly controlling FWER and FDR

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  • Edsel Peña
  • Joshua Habiger
  • Wensong Wu

Abstract

Two general classes of multiple decision functions, where each member of the first class strongly controls the family-wise error rate (FWER), while each member of the second class strongly controls the false discovery rate (FDR), are described. These classes offer the possibility that optimal multiple decision functions with respect to a pre-specified Type II error criterion, such as the missed discovery rate (MDR), could be found which control the FWER or FDR Type I error rates. The gain in MDR of the associated FDR-controlling procedure relative to the well-known Benjamini–Hochberg procedure is demonstrated via a modest simulation study with gamma-distributed component data. Such multiple decision functions may have the potential of being utilized in multiple testing, specifically in the analysis of high-dimensional data sets. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Edsel Peña & Joshua Habiger & Wensong Wu, 2015. "Classes of multiple decision functions strongly controlling FWER and FDR," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(5), pages 563-595, July.
    • Handle: RePEc:spr:metrik:v:78:y:2015:i:5:p:563-595
    DOI: 10.1007/s00184-014-0516-6
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    References listed on IDEAS

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    1. Sun, Wenguang & Cai, T. Tony, 2007. "Oracle and Adaptive Compound Decision Rules for False Discovery Rate Control," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 901-912, September.
    2. Christopher R. Genovese & Kathryn Roeder & Larry Wasserman, 2006. "False discovery control with p-value weighting," Biometrika, Biometrika Trust, vol. 93(3), pages 509-524, September.
    3. Michele Guindani & Peter Müller & Song Zhang, 2009. "A Bayesian discovery procedure," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 905-925, November.
    4. John D. Storey, 2007. "The optimal discovery procedure: a new approach to simultaneous significance testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 347-368, June.
    5. 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.
    6. Kang Guolian & Ye Keying & Liu Nianjun & Allison David B. & Gao Guimin, 2009. "Weighted Multiple Hypothesis Testing Procedures," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-24, April.
    7. Joshua Habiger & Edsel Peña, 2011. "Randomised -values and nonparametric procedures in multiple testing," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 583-604.
    8. Peter Muller & Giovanni Parmigiani & Christian Robert & Judith Rousseau, 2004. "Optimal Sample Size for Multiple Testing: The Case of Gene Expression Microarrays," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 990-1001, December.
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