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 discrete data with independent coordinates; furthermore, simulations indicate that it also performs well for discrete data with dependent coordinates, and that it outperforms alternative estimation methods. Consistency of the bootstrap is proved in the Kolmogorov distance as well as in the Wasserstein distance.