A New Coefficient of Correlation

By Sourav Chatterjee. Journal of the American Statistical Association, 2019

393 citations recorded by the source corpus.

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.

Subfields: Analytical Chemistry, Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f77327cbdff01313e548cd15e7d4c802685d26af

How researchers see this paper

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

In Analytical Chemistry

In Artificial Intelligence

In Statistics and Probability

Citations in the corpus

On boosting the power of Chatterjee’s rank correlation (2021, background): “Proposition 2.1 (Theorem 2 in Dette et al. (2013), Theorem 1.1 in Chatterjee (2021)).”
Measuring Association on Topological Spaces Using Kernels and Geometric Graphs (2020, methodology): “The authors would like to thank Huang Zhen for his careful reading of the paper and a number of insightful suggestions; and also Bhaswar Bhattacharya, Sourav Chatterjee, Holger Dette, Arthur Gretton, Marc Hallin, and Fang Han for helpful comments.”
On the power of Chatterjee’s rank correlation (2020, methodology): “For this, we contribute a new proof of Theorem 2.1 of Chatterjee (2020) via a development of Hájek’s representation as done by Angus (1995).”
Global Sensitivity Analysis: a new generation of mighty estimators based on rank statistics (2020, neutral): “In a recent work [7], Chatterjee studies the dependence between two variables by introducing an empirical correlation coefficient based on rank statistics, see Section 2.”
High-dimensional consistent independence testing with maxima of rank correlations (2018, background): “The only exception is a new rank correlation measure that was just proposed (Chatterjee, 2019), whose limiting distribution is normal.”
On Azadkia–Chatterjee’s conditional dependence coefficient (2021, methodology): “In this manuscript, we explore the use of Azadkia–Chatterjee’s conditional dependence coefficient in inferential tasks. Specifically, we adopt the framework of conditional randomization tests in order to study the power of Azadkia–Chatterjee-type tests of conditional independence. Our analyses take ”