标题： 多变量极值分布的最大似然估计的渐近性质 显示英文标题

标题： Asymptotic properties of the maximum likelihood estimator for multivariate extreme value distributions

摘要： 极值分布和过程是极端事件建模以及尾部风险评估的重要模型。 参数化极值分布的完全多元似然函数非常复杂，只有最近的进步才使其得以应用。 多元极值中最大似然估计量的渐近性质大多未知。 本文给出了极值分布指数函数和角测度的自然条件，以确保估计量的渐近正态性。 我们通过将其应用于多元极值统计中的流行参数模型和最常用的几类空间极值过程族，展示了该结果的有效性。 显示英文摘要

摘要： Max-stable distributions and processes are important models for extreme events and the assessment of tail risks. The full, multivariate likelihood of a parametric max-stable distribution is complicated and only recent advances enable its use. The asymptotic properties of the maximum likelihood estimator in multivariate extremes are mostly unknown. In this paper we provide natural conditions on the exponent function and the angular measure of the max-stable distribution that ensure asymptotic normality of the estimator. We show the effectiveness of this result by applying it to popular parametric models in multivariate extreme value statistics and to the most commonly used families of spatial max-stable processes.