On the power of Chatterjee rank correlation

Abstract

Chatterjee (2021) introduced a simple new rank correlation coefficient that has attracted much recent attention. 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 to three established rank correlations that also facilitate consistent tests of independence, namely, Hoeffding's $D$, Blum-Kiefer-Rosenblatt's $R$, and Bergsma-Dassios-Yanagimoto's ${\tau }^{\ast }$. We contrast their computational efficiency 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 sub-optimal compared to $D$, $R$, and ${\tau }^{\ast }$. The situation is more subtle for a related earlier estimator of Dette et al. (2013). These results favor $D$, $R$, and ${\tau }^{\ast }$ over Chatterjee's new correlation coefficient for the purpose of testing independence.

arXiv commentto appear in Biometrika

References in corpus (5)

• A consistent test of independence based on a sign covariance related to Kendall's tau
• Multivariate Rank-based Distribution-free Nonparametric Testing using Measure Transportation
• Correlations with tailored extremal properties
• Counting Small Permutation Patterns
• Computing the Bergsma Dassios sign-covariance

Cited by in corpus (3)

• Measuring Association on Topological Spaces Using Kernels and Geometric Graphs
• Correlations with tailored extremal properties
• independence: Fast Rank Tests