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:在单体数据中,有标准程序用于确定产生最大观测结果的主要特征,但在多变量环境中,情况则大相径庭。本文旨在提供各种工具和算法,以探测多变量数据中的主要方向组成部分。我们研究了维度为$d\geq 2美元的一般重尾多变量随机矢量,并提供了一致的估算值,可用于评价数据为何是重尾的。这是通过确定风险最大的方向组成部分来完成的。结果在制订再保险政策和对多个资产组合进行套期保值时对保险和融资特别有利。