On the power of Chatterjee rank correlation

Recently, Chatterjee (2020) introduced a new rank correlation that attracts many statisticians' attention. This paper compares it to three already well-used rank correlations in literature, Hoeffding's $D$, Blum-Kiefer-Rosenblatt's $R$, and Bergsma-Dassios-Yanagimoto's $\tau^*$. Three criteria are considered: (i) computational efficiency, (ii) consistency against fixed alternatives, and (iii) power against local alternatives. Our main results show the unfortunate rate sub-optimality of Chatterjee's rank correlation against three popular local alternatives in independence testing literature. Along with some recent computational breakthroughs, they favor the other three in many settings.