Assessing Dependence in Multivariate Heavy Tailed Data

Abstract: 

We review a framework for assessing dependence in multivariate data that could plausibly come from a multivariate power law. The framework is allows multiple (even infinite) heavy tail regimes depending on the choice of scaling and the definition of an extreme region. We use the framework to explore extremal dependence between components using graphical and analytical means. Tools include the diamond plot, support estimation plots and network plots with edges representing a measure of strength of dependence. Some examples from various disciplines are given.