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Randomised -values and nonparametric procedures in multiple testing

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  • Joshua Habiger
  • Edsel Peña

Abstract

The validity of many multiple hypothesis testing procedures for false discovery rate (FDR) control relies on the assumption that P-value statistics are uniformly distributed under the null hypotheses. However, this assumption fails if the test statistics have discrete distributions or if the distributional model for the observables is misspecified. A stochastic process framework is introduced that, with the aid of a uniform variate, admits P-value statistics to satisfy the uniformity condition even when test statistics have discrete distributions. This allows nonparametric tests to be used to generate P-value statistics satisfying the uniformity condition. The resulting multiple testing procedures are therefore endowed with robustness properties. Simulation studies suggest that nonparametric randomised test P-values allow for these FDR methods to perform better when the model for the observables is nonparametric or misspecified.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:3:p:583-604
    DOI: 10.1080/10485252.2010.482154
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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. Efron, Bradley, 2004. "Large-Scale Simultaneous Hypothesis Testing: The Choice of a Null Hypothesis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 96-104, January.
    3. Efron B. & Tibshirani R. & Storey J.D. & Tusher V., 2001. "Empirical Bayes Analysis of a Microarray Experiment," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1151-1160, December.
    4. 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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    Cited by:

    1. Anh-Tuan Hoang & Thorsten Dickhaus, 2022. "On the usage of randomized p-values in the Schweder–Spjøtvoll estimator," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 289-319, April.
    2. 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.
    3. 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.

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