From environmental sciences to finance, there are growing needs for assessing the risk of more extreme events than those observed. Extrapolating extreme events beyond the range of the data is not obvious and requires advanced tools based on extreme value theory. Furthermore, the complexity of risk assessments often requires the inclusion of multiple variables. Extreme value theory provides very important tools for the analysis of multivariate or spatial extreme events, but these are not easily accessible to professionals without appropriate expertise. This article provides a minimal background on multivariate and spatial extremes and gives simple yet thorough instructions to analyse high-dimensional extremes using the R package ExtremalDep. After briefly introducing the statistical methodologies, we focus on road testing the package's toolbox through several real-world applications.

翻译：从环境科学到金融领域，评估超出观测范围的极端事件风险的需求日益增长。将极端事件外推至数据范围之外并非易事，需要基于极值理论的先进工具。此外，风险评估的复杂性通常要求纳入多个变量。极值理论为多元或空间极端事件的分析提供了重要工具，但这些工具对于缺乏专业知识的从业者而言并不易掌握。本文提供了多元与空间极值的基础背景知识，并通过R包ExtremalDep给出了分析高维极值的简明而完整的操作指南。在简要介绍统计方法后，我们将重点通过多个实际应用案例对该软件包的工具箱进行实测检验。