Extreme-value theory has been explored in considerable detail for univariate and low-dimensional observations, but the field is still in an early stage regarding high-dimensional multivariate observations. In this paper, we focus on H\"usler-Reiss models and their domain of attraction, a popular class of models for multivariate extremes that exhibit some similarities to multivariate Gaussian distributions. We devise novel estimators for the parameters of this model based on score matching and equip these estimators with state-of-the-art theories for high-dimensional settings and with exceptionally scalable algorithms. We perform a simulation study to demonstrate that the estimators can estimate a large number of parameters reliably and fast; for example, we show that H\"usler-Reiss models with thousands of parameters can be fitted within a couple of minutes on a standard laptop.

翻译：极值理论已在单变量和低维观测中得到了相当详细的探讨，但针对高维多变量观测的研究仍处于早期阶段。本文聚焦于Hüsler-Reiss模型及其吸引域——这是一类与多元高斯分布存在若干相似性的流行多变量极值模型。我们基于分数匹配（score matching）为该模型设计了新型估计量，并为这些估计量配备了针对高维场景的最先进理论框架及高度可扩展的算法。通过模拟研究，我们证明这些估计量能够快速且可靠地估计大量参数；例如，利用标准笔记本电脑可在数分钟内完成含数千个参数的Hüsler-Reiss模型拟合。