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Large-Scale Multiple Testing of Correlations

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  • T. Tony Cai
  • Weidong Liu

Abstract

Multiple testing of correlations arises in many applications including gene coexpression network analysis and brain connectivity analysis. In this article, we consider large-scale simultaneous testing for correlations in both the one-sample and two-sample settings. New multiple testing procedures are proposed and a bootstrap method is introduced for estimating the proportion of the nulls falsely rejected among all the true nulls. We investigate the properties of the proposed procedures both theoretically and numerically. It is shown that the procedures asymptotically control the overall false discovery rate and false discovery proportion at the nominal level. Simulation results show that the methods perform well numerically in terms of both the size and power of the test and it significantly outperforms two alternative methods. The two-sample procedure is also illustrated by an analysis of a prostate cancer dataset for the detection of changes in coexpression patterns between gene expression levels. Supplementary materials for this article are available online.

Suggested Citation

  • T. Tony Cai & Weidong Liu, 2016. "Large-Scale Multiple Testing of Correlations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 229-240, March.
    • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:513:p:229-240
    DOI: 10.1080/01621459.2014.999157
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    References listed on IDEAS

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    9. 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.
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    6. Chen, Xin & Yang, Dan & Xu, Yan & Xia, Yin & Wang, Dong & Shen, Haipeng, 2023. "Testing and support recovery of correlation structures for matrix-valued observations with an application to stock market data," Journal of Econometrics, Elsevier, vol. 232(2), pages 544-564.

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