A new coefficient of correlation

TL;DR

This paper introduces a new correlation coefficient that is simple, interpretable, and consistent in measuring dependence, satisfying properties of classical coefficients without distributional assumptions.

Contribution

It presents a novel correlation coefficient that is as simple as classical ones but uniquely characterizes independence and dependence with straightforward asymptotic properties.

Findings

The coefficient equals 0 if and only if variables are independent.

It equals 1 if and only if one variable is a measurable function of the other.

No distributional assumptions are required for the coefficient's properties.

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.