A Basic Treatment of the Distance Covariance

The distance covariance of Sz\'ekely, et al. [23] and Sz\'ekely Rizzo [21], a powerful measure dependence between sets multivariate random variables, has the crucial feature that it equals zero if only are mutually independent. Hence can be applied to data detect arbitrary types non-linear associations variables. We provide in this article basic, albeit rigorous, introductory treatment covariance. Our investigations yield an approach used as foundation for presentation important timely topic even advanced undergraduate- or junior graduate-level courses on mathematical statistics.