On the power of Chatterjee’s rank correlation

By Hongjian Shi, Mathias Drton, Fang Han. Biometrika, 2020

74 citations recorded by the source corpus.

Chatterjee (2021+) introduced a simple new rank correlation coefficient that has attracted much recent attention. 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 to 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 τ *. We contrast their computational efficiency 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 sub-optimal compared to D, R, and τ *. The situation is more subtle for a related earlier estimator of Dette et al. (2013). These results favor D, R, and τ * over Chatterjee’s new correlation coefficient for the purpose of testing independence.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/384e576b3c12a2b1d1dc38d4f38daa77df776eaf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Zhexiao Lin
2. Fang Han

In Statistics and Probability

1. Zhexiao Lin
2. Fang Han
3. Mathias Drton
4. Hongjian Shi

Citations in the corpus

• On boosting the power of Chatterjee’s rank correlation (2021, background): “Indeed, recent results have exhibited that a test of independence based on Proposition 2.2(ii) is inefficient in common classes of smooth alternatives; cf. Cao and Bickel (2020) and Shi et al. (2021b).”