On the power of Chatterjee's rank correlation

• 成果类型: Article
• 署名作者: Shi, H.; Drton, M.; Han, F.
• 署名单位: University of Washington; University of Washington Seattle; Technical University of Munich
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asab028
• 发表日期: 2022
• 页码: 317333
• 关键词: INDEPENDENCE; association

摘要

Chatterjee (2021) introduced a simple new rank correlation coefficient that has attracted much attention recently. The coefficient has the unusual appeal that it not only estimates a population quantity first proposed by that is zero if and only if the underlying pair of random variables is independent, but also is asymptotically normal under independence. This paper compares Chatterjee's new correlation coefficient with three established rank correlations that also facilitate consistent tests of independence, namely Hoeffding's D, Blum-Kiefer-Rosenblatt's R, and Bergsma-Dassios-Yanagimoto's tau*. We compare the computational efficiency of these rank correlation coefficients in light of recent advances, and investigate their power against local rotation and mixture alternatives. Our main results show that Chatterjee's coefficient is unfortunately rate-suboptimal compared to D, R and tau*. The situation is more subtle for a related earlier estimator of Dette et al. (2013). These results favour D, R and tau* over Chatterjee's new correlation coefficient for the purpose of testing independence.