A New Coefficient of Correlation

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 variabl...

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Bibliographic Details
Published in:Journal of the American Statistical Association Vol. 116; no. 536; pp. 2009 - 2022
Main Author: Chatterjee, Sourav
Format: Journal Article
Language:English
Published: Alexandria Taylor & Francis 02.10.2021
Taylor & Francis Ltd
Subjects:
Americans
Asymptotic methods
Coefficients
Correlation
Independence
Independent variables
mathematical theory
Measure of association
Property
Regression analysis
Statistical methods
Statistics
Variables
ISSN:0162-1459, 1537-274X, 1537-274X
Online Access:Get full text
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Summary: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.
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ISSN:0162-1459
1537-274X
1537-274X
DOI:10.1080/01621459.2020.1758115