On the connections between Chatterjee's correlation and rank distance correlation

Thomas M. Menino Convention & Exhibition Center 

Distance correlation and Chatterjee's correlation are two highly representative measures of dependence. Their simplicity and desirable properties have attracted much attention over the past years, leading to numerous extensions and in-depth discussions. The theoretical connections between these two measures, however, have remained largely underexplored, despite some empirical comparisons of their statistical power. In this work, we investigate some connections between Chatterjee's correlation and the rank-based distance correlation. We show that both belong to a class of dependence measures based on non-negative weighted rank differences, but with distinct weight allocations resulting in different asymptotic null distributions. Motivated by this finding, we construct a new rank distance correlation using Gaussian kernel that, quite interestingly, exhibits Chatterjee-like behavior under finite sample and specific bandwidth conditions.

distance correlation

Chatterjee's correlation

non-negative weighted rank difference 

Section on Nonparametric Statistics