Conditional Distance Variance and Correlation

Recently a new dependence measure, the distance correlation, has been proposed to measure the dependence between continuous random variables. A nice property of this measure is that it can be consistently estimated with the empirical average of the products of certain distances between the sample points. Here we generalize this quantity to measure the conditional dependence between random variables, and show that this can also be estimated with a statistic using a weighted empirical average of the products of distances between the sample points. We demonstrate the applicability of the estimators with numerical experiments on real and simulated data sets.