标题： 似然估计量在多元极值分布中的渐近性质 显示英文标题

标题： Asymptotic properties of likelihood estimators for multivariate extreme value distributions

摘要： 最大稳定分布和过程是用于极端事件和尾部风险评估的重要模型。 参数化最大稳定分布的完整多变量似然函数较为复杂，只有近期的进展才使其能够在频率学派和贝叶斯统计中得到应用。 在多变量极值中，最大似然估计量和后验分布中位数的渐近性质大多未知。 在本文中，我们提供了关于最大稳定分布的指数函数和角度测度的自然条件，这些条件确保了这些似然估计量的渐近正态性。 我们通过将其应用于多变量极值统计中的流行参数模型以及最常使用的空间最大稳定过程族来展示该结果的有效性。 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 in both frequentist and Bayesian statistics. The asymptotic properties of the maximum likelihood estimator and the median of the posterior distribution 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 these likelihood estimators. 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.