On the power of Chatterjee rank correlation

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 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 $\tau^*$. We contrast their computational efficiency in light of recent advances, and investigate their power against local \nb{rotation and mixture} alternatives. Our main results show that Chatterjee's coefficient is unfortunately rate sub-optimal compared to $D$, $R$, and $\tau^*$. These results favor $D$, $R$, and $\tau^*$ over Chatterjee's new correlation coefficient for the purpose of testing independence.