In univariate data, there exist standard procedures for identifying dominating features that produce the largest observations. However, in the multivariate setting, the situation is quite different. This paper aims to provide tools and algorithms for detecting dominating directional components in multivariate data. We study general heavy-tailed multivariate random vectors in dimension $d\geq 2$ and present consistent estimators which can be used to evaluate why the data is heavy-tailed. This is done by identifying the set of the riskiest directional components. The results are of particular interest in insurance when setting reinsurance policies and in finance when hedging a portfolio of multiple assets.

翻译：在单变量数据中，存在用于识别产生最大观测值的支配性特征的标准程序。然而，在多变量情境下，情况颇为不同。本文旨在提供用于检测多元数据中支配性方向分量的工具与算法。我们研究维度 $d\geq 2$ 的一般重尾多元随机向量，并提出可用于评估数据为何呈重尾性的一致估计量。这通过识别最危险方向分量的集合来实现。该结果在保险领域制定再保险政策，以及在金融领域对冲多资产组合时具有特殊意义。