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

JOURNAL OF MULTIVARIATE ANALYSIS

卷:173

Article

Ho, Zhen Wai Olivier¹  Dombry, Clement¹ 

[1] Univ Bourgogne Franche Comte, Lab Math Besancon, UMR 6623, 16 Route Gray, F-25030 Besancon, France

关键词: Exponential family;    Extreme value theory;    Maximum likelihood estimation;    Regular variations;   

DOI  :  10.1016/j.jmva.2019.04.008

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free