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On the test of covariance between two high-dimensional random vectors

Author

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  • Yongshuai Chen

    (Capital University of Economics and Business
    Capital Normal University)

  • Wenwen Guo

    (Capital Normal University)

  • Hengjian Cui

    (Capital Normal University)

Abstract

We consider a problem of association test in high dimension. A new test statistic is proposed based on the covariance of random vectors and its asymptotic properties are derived under both the null hypothesis and the local alternatives. Furthermore power enhancement technique is utilized to boost the empirical power especially under sparse alternatives. We examine the finite-sample performances of the proposed test via Monte Carlo simulations, which show that the proposed test outperforms some existing procedures. An empirical analysis of a microarray data is demonstrated to detect the relationship between the genes.

Suggested Citation

  • Yongshuai Chen & Wenwen Guo & Hengjian Cui, 2024. "On the test of covariance between two high-dimensional random vectors," Statistical Papers, Springer, vol. 65(5), pages 2687-2717, July.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:5:d:10.1007_s00362-023-01500-6
    DOI: 10.1007/s00362-023-01500-6
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    References listed on IDEAS

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    6. Taskinen, Sara & Oja, Hannu & Randles, Ronald H., 2005. "Multivariate Nonparametric Tests of Independence," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 916-925, September.
    7. Shun Yao & Xianyang Zhang & Xiaofeng Shao, 2018. "Testing mutual independence in high dimension via distance covariance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(3), pages 455-480, June.
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