On the failure of the bootstrap for Chatterjee's rank correlation

TL;DR

This paper demonstrates that the standard bootstrap method is inconsistent for Chatterjee's rank correlation, providing theoretical proof and simulation evidence, and discusses valid alternative inference methods.

Contribution

The paper proves the bootstrap's failure for Chatterjee's rank correlation under independence and highlights alternative valid inference approaches.

Findings

Bootstrap is inconsistent for Chatterjee's rank correlation.

Chatterjee's correlation is asymptotically normal but bootstrap fails.

Valid inference can be done using original tests and asymptotic variance estimators.

Abstract

While researchers commonly use the bootstrap for statistical inference, many of us have realized that the standard bootstrap, in general, does not work for Chatterjee's rank correlation. In this paper, we provide proof of this issue under an additional independence assumption, and complement our theory with simulation evidence for general settings. Chatterjee's rank correlation thus falls into a category of statistics that are asymptotically normal but bootstrap inconsistent. Valid inferential methods in this case are Chatterjee's original proposal (for testing independence) and Lin and Han (2022)'s analytic asymptotic variance estimator (for more general purposes).