  Distance multivariance is a multivariate dependence measure, which can detect
dependencies between an arbitrary number of random vectors each of which can
have a distinct dimension. Here we discuss several new aspects, present a
concise overview and use it as the basis for several new results and concepts:
In particular, we show that distance multivariance unifies (and extends)
distance covariance and the Hilbert-Schmidt independence criterion HSIC,
moreover also the classical linear dependence measures: covariance, Pearson's
correlation and the RV coefficient appear as limiting cases. Based on distance
multivariance several new measures are defined: a multicorrelation which
satisfies a natural set of multivariate dependence measure axioms and
$m$-multivariance which is a dependence measure yielding tests for pairwise
independence and independence of higher order. These tests are computationally
feasible and under very mild moment conditions they are consistent against all
alternatives. Moreover, a general visualization scheme for higher order
dependencies is proposed, including consistent estimators (based on distance
multivariance) for the dependence structure.
  Many illustrative examples are provided. All functions for the use of
distance multivariance in applications are published in the R-package
'multivariance'.
