A Basic Treatment of the Distance Covariance

Abstract

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

12 pages, 2 figures

References in corpus (5)

• Measuring and testing dependence by correlation of distances
• Brownian distance covariance
• Interpreting the Distance Correlation Results for the COMBO-17 Survey
• Distance Correlation: A New Tool for Detecting Association and Measuring Correlation Between Data Sets
• A Statistically and Numerically Efficient Independence Test based on Random Projections and Distance Covariance