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Testing independence in high dimensions using Kendall’s tau

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  • Mao, Guangyu

Abstract

To check the total independence of a random vector without Gaussian assumption in high dimensions, Leung and Drton (forthcoming) recently developed a test by virtue of pairwise Kendall’s taus. However, as their simulation shows, the test suffers from noticeable size distortion when the sample size is small. The present paper provides a theoretical explanation about this phenomenon, and accordingly proposes a new test. The new test can be justified when both the dimension and the sample size go to infinity simultaneously, and moreover, it can be even justified when the dimension tends to infinity but the sample size is fixed, which implies that the test can perform well in the cases of small sample size. Simulation studies confirm the theoretical findings, and show that the newly proposed test can bring remarkable improvement. To illustrate the use of the new test, a real data set is also analyzed.

Suggested Citation

  • Mao, Guangyu, 2018. "Testing independence in high dimensions using Kendall’s tau," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 128-137.
    • Handle: RePEc:eee:csdana:v:117:y:2018:i:c:p:128-137
    DOI: 10.1016/j.csda.2017.07.012
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    References listed on IDEAS

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    1. Mao, Guangyu, 2014. "A new test of independence for high-dimensional data," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 14-18.
    2. Peter Hall & J. S. Marron & Amnon Neeman, 2005. "Geometric representation of high dimension, low sample size data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 427-444, June.
    3. 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.
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    6. Srivastava, Muni S. & Kollo, Tõnu & von Rosen, Dietrich, 2011. "Some tests for the covariance matrix with fewer observations than the dimension under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1090-1103, July.
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    Cited by:

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    3. Feng, Long & Zhao, Ping & Ding, Yanling & Liu, Binghui, 2021. "Rank-based tests of cross-sectional dependence in panel data models," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    4. Kai Xu & Minghui Yang, 2025. "A distance covariance test of independence in high dimension, low sample size contexts," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 77(5), pages 731-755, October.
    5. Xu, Kai & Cheng, Qing & He, Daojiang, 2025. "On summed nonparametric dependence measures in high dimensions, fixed or large samples," Computational Statistics & Data Analysis, Elsevier, vol. 205(C).
    6. Long Feng & Yanling Ding & Binghui Liu, 2020. "Rank‐based Tests for Cross‐sectional Dependence in Large (N, T) Fixed Effects Panel Data Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(5), pages 1198-1216, October.
    7. Ivair R. Silva & Yan Zhuang & Julio C. A. da Silva Junior, 2022. "Kronecker delta method for testing independence between two vectors in high-dimension," Statistical Papers, Springer, vol. 63(2), pages 343-365, April.
    8. 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).
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    11. Liqi Xia & Ruiyuan Cao & Jiang Du & Jun Dai, 2025. "Consistent complete independence test in high dimensions based on Chatterjee correlation coefficient," Statistical Papers, Springer, vol. 66(1), pages 1-32, January.

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