On the power of Chatterjee’s rank correlation

Adaptive test of independence based on HSIC measures

H Shi, M Drton and F Han

Biometrika, 2022, vol. 109, issue 2, 317-333

Abstract: SummaryChatterjee (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 Dette et al. (2013) 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 , Blum–Kiefer–Rosenblatt’s , and Bergsma–Dassios–Yanagimoto’s . 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 ,and . The situation is more subtle for a related earlier estimator of Dette et al. (2013). These results favour ,andover Chatterjee’s new correlation coefficient for the purpose of testing independence.

Keywords: Dependence measure; Independence test; Le Cam’s third lemma; Rank correlation; Rate-optimality (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (5)

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