“On Boosting the Power of Chatterjee’s Rank Correlation”, Zhexiao Lin, Fang Han2021-08-15 (order statistics; backlinks; similar)⁠:

Chatterjee2021’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 unusual property of being 0–1, 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 & Bickel2020; Shi et al 2021b) 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 revised Chatterjee’s rank correlations that still consistently estimate the same dependence measure but provably achieve near-parametric efficiency in testing against Gaussian rotation alternatives. This is possible via incorporating many right nearest neighbors in constructing the correlation coefficients.

We thus overcome the “only one disadvantage” of Chatterjee’s rank correlation (Chatterjee, 2021, §7).

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