A Simple Bootstrap for Chatterjee's Rank Correlation

TL;DR

This paper establishes the consistency of an $m$ out of $n$ bootstrap procedure for Chatterjee's rank correlation across various data types, supported by theoretical proofs and simulations showing its effectiveness and superiority over other methods.

Contribution

It proves the bootstrap's consistency for Chatterjee's rank correlation in both continuous and discrete data, extending its applicability and demonstrating its practical performance.

Findings

Bootstrap is consistent for continuous data.

Bootstrap performs well for discrete data with dependent coordinates.

It outperforms alternative estimation methods in simulations.

Abstract

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 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 as well as in the Wasserstein distance.