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On the power of Chatterjee’s rank correlation
[Adaptive test of independence based on HSIC measures]

Author

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  • H Shi
  • M Drton
  • F Han

Abstract

SummaryChatterjee (2021) introduced a simple new rank correlation coefficient that has attracted much attention recently. The coefficient has the unusual appeal that it not only estimates a population quantity first proposed by Dette et al. (2013) that is zero if and only if the underlying pair of random variables is independent, but also is asymptotically normal under independence. This paper compares Chatterjee’s new correlation coefficient with three established rank correlations that also facilitate consistent tests of independence, namely Hoeffding’s , Blum–Kiefer–Rosenblatt’s , and Bergsma–Dassios–Yanagimoto’s . We compare the computational efficiency of these rank correlation coefficients in light of recent advances, and investigate their power against local rotation and mixture alternatives. Our main results show that Chatterjee’s coefficient is unfortunately rate-suboptimal compared to ,and . The situation is more subtle for a related earlier estimator of Dette et al. (2013). These results favour ,andover Chatterjee’s new correlation coefficient for the purpose of testing independence.

Suggested Citation

  • H Shi & M Drton & F Han, 2022. "On the power of Chatterjee’s rank correlation [Adaptive test of independence based on HSIC measures]," Biometrika, Biometrika Trust, vol. 109(2), pages 317-333.
    • Handle: RePEc:oup:biomet:v:109:y:2022:i:2:p:317-333.
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    File URL: http://hdl.handle.net/10.1093/biomet/asab028
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    References listed on IDEAS

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    1. Holger Dette & Karl F. Siburg & Pavel A. Stoimenov, 2013. "A Copula-Based Non-parametric Measure of Regression Dependence," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(1), pages 21-41, March.
    2. Sourav Chatterjee, 2021. "A New Coefficient of Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 2009-2022, October.
    3. Hongjian Shi & Marc Hallin & Mathias Drton & Fang Han, 2020. "Rate-Optimality of Consistent Distribution-Free Tests of Independence Based on Center-Outward Ranks and Signs," Working Papers ECARES 2020-23, ULB -- Universite Libre de Bruxelles.
    4. L Weihs & M Drton & N Meinshausen, 2018. "Symmetric rank covariances: a generalized framework for nonparametric measures of dependence," Biometrika, Biometrika Trust, vol. 105(3), pages 547-562.
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    Cited by:

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    3. Zhang, Qingyang, 2023. "On the asymptotic null distribution of the symmetrized Chatterjee’s correlation coefficient," Statistics & Probability Letters, Elsevier, vol. 194(C).
    4. Zhexiao Lin & Fang Han, 2023. "On the failure of the bootstrap for Chatterjee's rank correlation," Papers 2303.14088, arXiv.org, revised Apr 2023.
    5. Reza Salimi & Kamran Pakizeh, 2024. "The extension of Pearson correlation coefficient, measuring noise, and selecting features," Papers 2402.00543, arXiv.org.
    6. R. Grübel, 2024. "Ranks, copulas, and permutons," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(2), pages 155-182, February.
    7. Fang Han, 2024. "An Introduction to Permutation Processes (version 0.5)," Papers 2407.09664, arXiv.org.

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