We consider a model for multivariate data with heavy-tailed marginals and a Gaussian dependence structure. The marginal distributions are allowed to have non-homogeneous tail behavior which is in contrast to most popular modeling paradigms for multivariate heavy-tails. Estimation and analysis in such models have been limited due to the so-called asymptotic tail independence property of Gaussian copula rendering probabilities of many relevant extreme sets negligible. In this paper we obtain precise asymptotic expressions for these erstwhile negligible probabilities. We also provide consistent estimates of the marginal tail indices and the Gaussian correlation parameters, and, establish their joint asymptotic normality. The efficacy of our estimation methods are exhibited using extensive simulations as well as real data sets from online networks, insurance claims, and internet traffic.

翻译：我们考虑一种具有重尾边缘分布和高斯相依结构的多变量数据模型。与大多数多变量重尾建模范式不同，该模型允许边缘分布呈现非齐次尾部行为。由于高斯连接函数具有所谓的渐近尾部独立性质，使得许多相关极端集合的概率可忽略不计，导致此类模型的估计与分析长期受限。本文首次获得了这些曾经可忽略概率的精确渐近表达式，并提供了边缘尾部指数与高斯相关参数的一致估计量，同时建立了其联合渐近正态性。通过大规模数值模拟以及来自在线网络、保险索赔和互联网流量的真实数据集，验证了我们估计方法的有效性。