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On boosting the power of Chatterjee’s rank correlation

Author

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  • Z Lin
  • F Han

Abstract

SummaryThe ingenious approach of Chatterjee (2021) to estimate a measure of dependence first proposed by Dette et al. (2013) based on simple rank statistics has quickly caught attention. This measure of dependence has the appealing property of being between 0 and 1, and being 0 or 1 if and only if the corresponding pair of random variables is independent or one is a measurable function of the other almost surely. However, more recent studies (Cao & Bickel 2020; Shi et al. 2022b) showed that independence tests based on Chatterjee’s rank correlation are unfortunately rate inefficient against various local alternatives and they call for variants. We answer this call by proposing an improvement to Chatterjee’s rank correlation that still consistently estimates the same dependence measure, but provably achieves near-parametric efficiency in testing against Gaussian rotation alternatives. This is possible by incorporating many right nearest neighbours in constructing the correlation coefficients. We thus overcome the ‘ only one disadvantage’ of Chatterjee’s rank correlation (Chatterjee, 2021, § 7).

Suggested Citation

  • Z Lin & F Han, 2023. "On boosting the power of Chatterjee’s rank correlation," Biometrika, Biometrika Trust, vol. 110(2), pages 283-299.
    • Handle: RePEc:oup:biomet:v:110:y:2023:i:2:p:283-299.
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    File URL: http://hdl.handle.net/10.1093/biomet/asac048
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    Cited by:

    1. Yihui He & Fang Han, 2023. "On propensity score matching with a diverging number of matches," Papers 2310.14142, arXiv.org, revised Nov 2023.
    2. Fang Han, 2024. "An Introduction to Permutation Processes (version 0.5)," Papers 2407.09664, arXiv.org.

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