On boosting the power of Chatterjee’s rank correlation

By Zhexiao Lin, Fang Han. Biometrika, 2021

63 citations recorded by the source corpus.

Chatterjee (2021)’s ingenious approach to estimating 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., 2022) 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, Section 7).

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5a6422cdba6fefc9fcf47d3013c345d7f297faef

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Citations in the corpus

On Azadkia–Chatterjee’s conditional dependence coefficient (2021, methodology): “…constructing the nearest neighbor graphs; see Bhattacharya (2019, Proposition 1), Deb et al. (2020, Remark 4.3), and in particular, a recent preprint by Lin and Han (2022b) on boosting the power of Chatterjee’s original proposal which however cannot be directly applied to multidimensional cases.”