In risk quantification of extreme events in multiple dimensions, a correct specification of the dependence structure among variables is difficult due to the limited size of effective data. This paper studies the problem of estimating quantiles for bivariate extreme value distributions, considering that an estimated Pickands dependence function may deviate from the truth within some fixed distance. Our method thus finds optimal upper and lower bounds for the true but unknown dependence function, based on which robust quantile bounds are obtained. A simulation study shows the usefulness of our robust estimates that can supplement traditional error estimation methods.

中文翻译：

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双变量极值模型下的稳健分位数估计

在多维多维极端事件的风险量化中，由于有效数据的大小有限，很难正确定义变量之间的依存结构。考虑到估计的Pickands依赖函数可能在某个固定距离内偏离真相，本文研究了估计二元极值分布的分位数的问题。因此，我们的方法找到了真实但未知的依赖函数的最佳上限和下限，并以此为基础获得了稳健的分位数界限。仿真研究表明，我们的鲁棒估计可以补充传统的误差估计方法，因此很有用。