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Testing and support recovery of multiple high-dimensional covariance matrices with false discovery rate control

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  • Yin Xia

    (Fudan University)

Abstract

Motivated by applications in genomics, we study in this paper four interrelated high-dimensional hypothesis testing problems on dependence structures among multiple populations. A new test statistic is constructed for testing the global hypothesis that multiple covariance matrices are equal, and its limiting null distribution is established. Correction methods are introduced to improve the accuracy of the test for finite samples. It is shown that the proposed tests are powerful against sparse alternatives and enjoy certain optimality properties. We then propose a multiple testing procedure for simultaneously testing the equality of the entries of the covariance matrices across multiple populations. The proposed method is shown to control the false discovery rate. A simulation study demonstrates that the proposed tests maintain the desired error rates under the null and have good power under the alternative. The methods are also applied to a Novartis multi-tissue analysis. In addition, testing and support recovery of submatrices of multiple covariance matrices are studied.

Suggested Citation

  • Yin Xia, 2017. "Testing and support recovery of multiple high-dimensional covariance matrices with false discovery rate control," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 782-801, December.
    • Handle: RePEc:spr:testjl:v:26:y:2017:i:4:d:10.1007_s11749-017-0533-7
    DOI: 10.1007/s11749-017-0533-7
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    References listed on IDEAS

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    1. Yin Xia & Tianxi Cai & T. Tony Cai, 2015. "Testing differential networks with applications to the detection of gene-gene interactions," Biometrika, Biometrika Trust, vol. 102(2), pages 247-266.
    2. Shen, Yanfeng & Lin, Zhengyan & Zhu, Jun, 2011. "Shrinkage-based regularization tests for high-dimensional data with application to gene set analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2221-2233, July.
    3. Srivastava, Muni S. & Yanagihara, Hirokazu, 2010. "Testing the equality of several covariance matrices with fewer observations than the dimension," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1319-1329, July.
    4. Tony Cai & Weidong Liu & Yin Xia, 2013. "Two-Sample Covariance Matrix Testing and Support Recovery in High-Dimensional and Sparse Settings," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 265-277, March.
    5. Wenguang Sun & T. Tony Cai, 2009. "Large‐scale multiple testing under dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 393-424, April.
    6. 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.
    7. Wenguang Sun & Brian J. Reich & T. Tony Cai & Michele Guindani & Armin Schwartzman, 2015. "False discovery control in large-scale spatial multiple testing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 59-83, January.
    8. John D. Storey & Jonathan E. Taylor & David Siegmund, 2004. "Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: a unified approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 187-205, February.
    9. Chen, Songxi, 2012. "Two Sample Tests for High Dimensional Covariance Matrices," MPRA Paper 46026, University Library of Munich, Germany.
    10. Cai, T. Tony & Xia, Yin, 2014. "High-dimensional sparse MANOVA," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 174-196.
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