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Estimation of the proportion of true null hypotheses in high-dimensional data under dependence

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  • Friguet, Chloé
  • Causeur, David

Abstract

In multiple testing, a challenging issue is to provide an accurate estimation of the proportion [pi]0 of true null hypotheses among the whole set of tests. Besides a biological interpretation, this parameter is involved in the control of error rates such as the False Discovery Rate. Improving its estimation can result in more powerful/less conservative methods of differential analysis. Various methods for [pi]0 estimation have been previously developed. Most of them rely on the assumption of independent p-values distributed according to a two-component mixture model, with a uniform distribution for null p-values. In a general factor analytic framework, the impact of dependence on the properties of the estimation procedures is first investigated and exact expressions of bias and variance are provided in case of dependent data. A more accurate factor-adjusted estimator of [pi]0 is finally presented, which shows large improvements with respect to the standard procedures.

Suggested Citation

  • Friguet, Chloé & Causeur, David, 2011. "Estimation of the proportion of true null hypotheses in high-dimensional data under dependence," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2665-2676, September.
  • Handle: RePEc:eee:csdana:v:55:y:2011:i:9:p:2665-2676
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    References listed on IDEAS

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    1. Robin, Stephane & Bar-Hen, Avner & Daudin, Jean-Jacques & Pierre, Laurent, 2007. "A semi-parametric approach for mixture models: Application to local false discovery rate estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5483-5493, August.
    2. Friguet, Chloé & Kloareg, Maela & Causeur, David, 2009. "A Factor Model Approach to Multiple Testing Under Dependence," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1406-1415.
    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. Nguyen, Danh V., 2004. "On estimating the proportion of true null hypotheses for false discovery rate controlling procedures in exploratory DNA microarray studies," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 611-637, October.
    5. Donald Rubin & Dorothy Thayer, 1982. "EM algorithms for ML factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 47(1), pages 69-76, March.
    6. 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.
    7. 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.
    8. Efron, Bradley, 2007. "Correlation and Large-Scale Simultaneous Significance Testing," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 93-103, March.
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    Cited by:

    1. Axel Gandy & Georg Hahn, 2016. "A Framework for Monte Carlo based Multiple Testing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 1046-1063, December.

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