A New Coefficient of Correlation. Issue 536 (2nd October 2021)

• Record Type: Journal Article
• Authors: Chatterjee, Sourav
• Is Part Of: Journal of the American Statistical Association. Volume 116:Issue 536(2021)
• Page Start: 2009
• Page End: 2022
• Publication Date: 2021-10-02
• Subjects: Correlation -- Independence -- Measure of association; Statistics -- Periodicals; Statistics -- Periodicals; Statistiques -- Périodiques; États-Unis -- Statistiques -- Périodiques; 519.5
• DOI: 10.1080/01621459.2020.1758115
• Languages: English
• ISSNs: 0162-1459

Abstract

Abstract : Abstract– Is it possible to define a coefficient of correlation which is (a) as simple as the classical coefficients like Pearson's correlation or Spearman's correlation, and yet (b) consistently estimates some simple and interpretable measure of the degree of dependence between the variables, which is 0 if and only if the variables are independent and 1 if and only if one is a measurable function of the other, and (c) has a simple asymptotic theory under the hypothesis of independence, like the classical coefficients? This article answers this question in the affirmative, by producing such a coefficient. No assumptions are needed on the distributions of the variables. There are several coefficients in the literature that converge to 0 if and only if the variables are independent, but none that satisfy any of the other properties mentioned above. Supplementary materials for this article are available online.