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A conservative estimator for the proportion of false nulls based on Dvoretzky, Kiefer and Wolfowitz inequality

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  • Farcomeni, Alessio
  • Pacillo, Simona

Abstract

We propose a simple estimator for the weight in a two-component mixture model between a known and an unknown density. We make no parametric assumptions about the unknown component and estimate the weight conservatively, i.e., the estimate is smaller than the true value with high probability. A brief simulation is used to compare the proposal with already available conservative approaches.

Suggested Citation

  • Farcomeni, Alessio & Pacillo, Simona, 2011. "A conservative estimator for the proportion of false nulls based on Dvoretzky, Kiefer and Wolfowitz inequality," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1867-1870.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:12:p:1867-1870
    DOI: 10.1016/j.spl.2011.07.017
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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. Alessio Farcomeni, 2006. "More Powerful Control of the False Discovery Rate Under Dependence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(1), pages 43-73, May.
    5. 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. Guillermo Durand & Gilles Blanchard & Pierre Neuvial & Etienne Roquain, 2020. "Post hoc false positive control for structured hypotheses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1114-1148, December.

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