Dependence structures - estimation and visualization using distance multivariance

Distance multivariance was recently introduced as a measure of multivariate dependence. Here we discuss several new aspects and present a guide to its use. In particular, $m$-multivariance is defined, which is a new dependence measure yielding tests for pairwise independence and independence of higher order. These tests are computationally feasible and under mild moment conditions they are consistent against all alternatives. Based on distance multivariance we also propose a visualization scheme for higher order dependence which fits into/extends the framework of probabilistic graphical models. Finally, resampling tests are introduced and it is indicated by several simulation studies that distance multivariance and the new measures match or outperform other recently introduced multivariate independence measures. Many examples are included. All functions for the use of distance multivariance in applications are published in the R-package 'multivariance'.