We consider multivariate extreme value statistics for independent but nonidentically distributed random vectors. In particular, the data may have varying tail copulas and also heteroscedastic marginal distributions. Assuming smoothly changing tail copulas, we propose a nonparametric estimator for the integrated tail copula and establish its asymptotic behavior. Notably, the heteroscedastic marginals do not affect the limiting processes. We use the main result for the integrated tail copula to test for a constant tail copula across all observations. Finally, a simulation study shows the good finite-sample behavior of our limit theorems as well as high power of the test.

翻译：我们考虑独立但非同分布随机向量的多元极值统计问题。具体而言，数据可能具有变化的尾部Copula函数以及异方差的边际分布。在假设尾部Copula函数平滑变化的条件下，我们提出了一种积分尾部Copula的非参数估计量，并建立了其渐近性质。值得注意的是，异方差边际分布不影响极限过程。我们利用积分尾部Copula的该主要结果来检验所有观测值是否具有恒定尾部Copula函数。最后，模拟研究表明，我们的极限定理具有良好的有限样本表现，且该检验具有较高的检验功效。