Multivariate extreme value analysis quantifies the probability and magnitude of joint extreme events. River discharges from the upper Danube River basin provide a challenging dataset for such analysis because the data, which is measured on a spatial network, exhibits both asymptotic dependence and asymptotic independence. To account for both features, we extend the conditional multivariate extreme value model (CMEVM) with a new approach for the residual distribution. This allows sparse (graphical) dependence structures and fully parametric prediction. Our approach fills a current gap in statistical methodology for graphical extremes, where existing models require asymptotic independence. Further, the model can be used to learn the graphical dependence structure when it is unknown a priori. To support inference in high dimensions, we propose a stepwise inference procedure that is computationally efficient and loses no information or predictive power. We show our method is flexible and accurately captures the extremal dependence for the upper Danube River basin discharges.

翻译：多元极值分析旨在量化联合极端事件的概率与强度。多瑙河上游流域的河流流量数据为此类分析提供了具有挑战性的研究对象，因为这一在空间网络上测量的数据集同时呈现渐近依赖与渐近独立特征。为兼顾这两种特性，我们通过一种新的残差分布方法扩展了条件多元极值模型（CMEVM）。该扩展支持稀疏（图结构）依赖关系与全参数化预测。我们的方法填补了当前图结构极值统计方法学的空白——现有模型均要求数据满足渐近独立性。此外，该模型可在先验依赖结构未知时学习图依赖关系。为支持高维推断，我们提出了一种计算高效且不损失信息或预测能力的逐步推断流程。实验表明，我们的方法能灵活准确地刻画多瑙河上游流域流量的极值依赖特性。