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Lower bounds for the number of false null hypotheses for multiple testing of associations under general dependence structures

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  • Nicolai Meinshausen
  • Peter Buhlmann

Abstract

We propose probabilistic lower bounds for the number of false null hypotheses when testing multiple hypotheses of association simultaneously. The bounds are valid under general and unknown dependence structures between the test statistics. The power of the proposed estimator to detect the full proportion of false null hypotheses is discussed and compared to other estimators. The proposed estimator is shown to deliver a tight probabilistic lower bound for the number of false null hypotheses in a multiple testing situation even under strong dependence between test statistics. Copyright 2005, Oxford University Press.

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  • Nicolai Meinshausen & Peter Buhlmann, 2005. "Lower bounds for the number of false null hypotheses for multiple testing of associations under general dependence structures," Biometrika, Biometrika Trust, vol. 92(4), pages 893-907, December.
    • Handle: RePEc:oup:biomet:v:92:y:2005:i:4:p:893-907
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    File URL: http://hdl.handle.net/10.1093/biomet/92.4.893
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    Cited by:

    1. Van Hanh Nguyen & Catherine Matias, 2014. "On Efficient Estimators of the Proportion of True Null Hypotheses in a Multiple Testing Setup," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1167-1194, December.
    2. X. Jessie Jeng & Huimin Peng & Wenbin Lu, 2021. "Model Selection With Mixed Variables on the Lasso Path," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 170-184, May.
    3. Jesse Hemerik & Jelle J. Goeman, 2021. "Another Look at the Lady Tasting Tea and Differences Between Permutation Tests and Randomisation Tests," International Statistical Review, International Statistical Institute, vol. 89(2), pages 367-381, August.
    4. Jesse Hemerik & Jelle Goeman, 2018. "Exact testing with random permutations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 811-825, December.
    5. Helmut Finner & Veronika Gontscharuk, 2009. "Controlling the familywise error rate with plug‐in estimator for the proportion of true null hypotheses," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 1031-1048, November.
    6. Rohit Kumar Patra & Bodhisattva Sen, 2016. "Estimation of a two-component mixture model with applications to multiple testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 869-893, September.
    7. Davide Risso & Liam Purvis & Russell B Fletcher & Diya Das & John Ngai & Sandrine Dudoit & Elizabeth Purdom, 2018. "clusterExperiment and RSEC: A Bioconductor package and framework for clustering of single-cell and other large gene expression datasets," PLOS Computational Biology, Public Library of Science, vol. 14(9), pages 1-16, September.

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