Speaker
Description
One of the oldest and classic statistical problems is the comparison of two groups by taking the difference of some characteristic of their underlying distributions. In this work we introduce a method for deriving a measure of dependence between two continuous random variables, X and Y, by taking the expected value of such a difference over all pairwise distributions of Y conditional on X. This method can therefore be used to derive measures of dependence between continuous variables from measures of pairwise differences between two distributions. We first show that several classical and more recent measures of dependence can be seen as special cases of this approach. We then show under what circumstances our novel method coincides with already existing methods. Finally we show how to construct new measures of dependence using our procedure. We show under which conditions these are true measures of dependence in the sense that they take values between 0 and 1, with 0 being attained only under independence and 1 being attained only under complete dependence, i.e. when Y is a measurable function of X. We provide a copula based approach for estimating these measures and prove the consistency of the estimator. Finally we present a simulation study to get an idea of the rate of convergence and the variance of the estimator, as well as a real-life data example for which our method can be used.
