A Simple Bootstrap for Chatterjee's Rank Correlation
Conference
65th ISI World Statistics Congress 2025
Format: IPS Abstract - WSC 2025
Keywords: bootstrap, dependence, rank
Session: IPS 1040 - Resampling Methods and Structural Disorders
Tuesday 7 October 10:50 a.m. - 12:30 p.m. (Europe/Amsterdam)
Abstract
Chatterjee's rank correlation is a new rank-based measure of association that is currently enjoying considerable interest in the statistical community due to its many desirable properties, but also poses some challenges. First, it is difficult to derive a limiting distribution. Second, and perhaps more unusual, it is known that the usual n out of n bootstrap fails, even under the assumption of asymptotic normality. We solve both problems by proving that Chatterjee's rank correlation is always asymptotically normal, and by presenting an m out of n bootstrap which is not only consistent, but outperforms alternative estimation methods. Consistency of the bootstrap holds in the Kolmogorov as well as in the Wasserstein distance.