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Generalized Schott type tests for complete independence in high dimensions

Author

Listed:
  • He, Daojiang
  • Liu, Huanyu
  • Xu, Kai
  • Cao, Mingxiang

Abstract

In the high dimensional setting, this article explores the problem of testing the complete independence of random variables having a multivariate normal distribution. A natural high-dimensional extension of the test in Schott (2005) is proposed for this purpose. The newly defined tests are asymptotically distribution-free as both the sample size and the number of variables go to infinity and hence have well-known critical values, accommodate situations where the number of variables is not small relative to the sample size and are applicable without specifying an explicit relationship between the number of variables and the sample size. In practice, as the true alternative hypothesis is unknown, it is unclear how to choose a powerful test. For this, we further propose an adaptive test that maintains high power across a wide range of situations. An extensive simulation study shows that the newly proposed tests are comparable to, and in many cases more powerful than, existing tests currently in the literature.

Suggested Citation

  • He, Daojiang & Liu, Huanyu & Xu, Kai & Cao, Mingxiang, 2021. "Generalized Schott type tests for complete independence in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:jmvana:v:183:y:2021:i:c:s0047259x21000099
    DOI: 10.1016/j.jmva.2021.104731
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    References listed on IDEAS

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    1. James R. Schott, 2005. "Testing for complete independence in high dimensions," Biometrika, Biometrika Trust, vol. 92(4), pages 951-956, December.
    2. Chen, Songxi, 2012. "Two Sample Tests for High Dimensional Covariance Matrices," MPRA Paper 46026, University Library of Munich, Germany.
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    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. T. Tony Cai & Weidong Liu & Yin Xia, 2014. "Two-sample test of high dimensional means under dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(2), pages 349-372, March.
    6. Mao, Guangyu, 2014. "A new test of independence for high-dimensional data," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 14-18.
    7. Guangyu Mao, 2017. "Robust test for independence in high dimensions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(20), pages 10036-10050, October.
    8. Wang, Guanghui & Zou, Changliang & Wang, Zhaojun, 2013. "A necessary test for complete independence in high dimensions using rank-correlations," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 224-232.
    9. Mao, Guangyu, 2018. "Testing independence in high dimensions using Kendall’s tau," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 128-137.
    10. Mao, Guangyu, 2015. "A note on testing complete independence for high dimensional data," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 82-85.
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