2017/12/26 by Zhen Wai Olivier Ho, Ho, Zhen Wai Olivier, Clément Dombry +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #Financial Risk and Volatility Modeling #Statistical Distribution Estimation and Applications
paper · pdf · doi:10.48550/arxiv.1712.09225
We revisit multivariate extreme value theory modeling by emphasizing multivariate regular variations and the multivariate Breiman 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 Hüsler-Reiss models. In a second part of the paper, we focus on the Hüsler-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 also consider the generalized Hüsler-Reiss Pareto model with different tail indices and a likelihood ratio test for discriminating constant tail index versus varying tail indices.