  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.
