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On a rank-based Azadkia-Chatterjee correlation coefficient

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arxiv 2412.02668 v1 pith:BKNV63SL submitted 2024-12-03 math.ST stat.TH

Leon Tran , Fang Han This is my paper · ORCID
classification math.STstat.TH
keywords coefficientcorrelationrank-basedazadkiaazadkia-chatterjeechatterjeegraphaddresses
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Azadkia and Chatterjee (Azadkia and Chatterjee, 2021) recently introduced a graph-based correlation coefficient that has garnered significant attention. The method relies on a nearest neighbor graph (NNG) constructed from the data. While appealing in many respects, NNGs typically lack the desirable property of scale invariance; that is, changing the scales of certain covariates can alter the structure of the graph. This paper addresses this limitation by employing a rank-based NNG proposed by Rosenbaum (2005) and gives necessary theoretical guarantees for the corresponding rank-based Azadkia-Chatterjee correlation coefficient.

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  1. Spectral analysis of large dimensional Chatterjee's rank correlation matrix

    math.ST 2025-10 conditional novelty 8.0 of 10

    A symmetrized Chatterjee rank correlation matrix has a semicircle spectral limit, plus a central limit theorem and independence tests that detect zero-linear-correlation dependence.

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