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Homogeneity Test of Multi-Sample Covariance Matrices in High Dimensions

Author

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  • Peng Sun

    (Department of Statistics, East China Normal University, Shanghai 200062, China
    KLATASDS-MOE, School of Statistics, East China Normal University, Shanghai 200062, China
    Center for Quantitative Medicine, Duke-NUS Medical School, Singapore 169857, Singapore)

  • Yincai Tang

    (Department of Statistics, East China Normal University, Shanghai 200062, China
    KLATASDS-MOE, School of Statistics, East China Normal University, Shanghai 200062, China)

  • Mingxiang Cao

    (School of Mathematics and Statistics, Anhui Normal University, Anhui 241002, China)

Abstract

In this paper, a new test statistic based on the weighted Frobenius norm of covariance matrices is proposed to test the homogeneity of multi-group population covariance matrices. The asymptotic distributions of the proposed test under the null and the alternative hypotheses are derived, respectively. Simulation results show that the proposed test procedure tends to outperform some existing test procedures.

Suggested Citation

  • Peng Sun & Yincai Tang & Mingxiang Cao, 2022. "Homogeneity Test of Multi-Sample Covariance Matrices in High Dimensions," Mathematics, MDPI, vol. 10(22), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4339-:d:977397
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    References listed on IDEAS

    as
    1. 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.
    2. Chen, Song Xi & Qin, Yingli, 2010. "A Two Sample Test for High Dimensional Data with Applications to Gene-set Testing," MPRA Paper 59642, University Library of Munich, Germany.
    3. Schott, James R., 2007. "A test for the equality of covariance matrices when the dimension is large relative to the sample sizes," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6535-6542, August.
    4. Chao Zhang & Zhidong Bai & Jiang Hu & Chen Wang, 2018. "Multi-sample test for high-dimensional covariance matrices," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(13), pages 3161-3177, July.
    Full references (including those not matched with items on IDEAS)

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