A Simple Bootstrap for Chatterjee's Rank Correlation

We prove that an $m$ out of $n$ bootstrap procedure for Chatterjee's rank correlation is consistent whenever asymptotic normality of Chatterjee's rank correlation can be established. In particular, we prove that $m$ out of $n$ bootstrap works for continuous as well as for discrete and independent data; furthermore, simulations indicate that it also performs well for discrete and dependent data, and that it outperforms alternative estimation methods.