Simple models for multivariate regular variation and the Husler-Reiss Pareto distribution

We revisit multivariate extreme-value theory modeling by emphasizing multivariate regular variation and a multivariate version of Breiman's Lemma. This allows us to recover in a simple framework the most popular multivariate extreme-value distributions, such as the logistic, negative logistic, Dirichlet, extremal- t and Husler-Reiss models. We then focus on the Husler-Reiss Pareto model and its surprising exponential family property. After a thorough study of this exponential family structure, we focus on maximum likelihood estimation: we prove the existence of asymptotically normal maximum likelihood estimators and provide simulation experiments assessing their finite-sample properties. We also consider the generalized Husler-Reiss Pareto model with different tail indices and a likelihood ratio test for discriminating constant tail index versus varying tail indices. (C) 2019 Elsevier Inc. All rights reserved.