All characterizations of non-degenerate multivariate tail dependence structures are both functional and infinite-dimensional. Taking advantage of the Hoeffding–Sobol decomposition, we derive new indices to measure and summarize the strength of dependence in a multivariate extreme value analysis. The tail superset importance coefficients provide a pairwise ordering of the asymptotic dependence structure. We then define the tail dependograph, which visually ranks the extremal dependence between the components of the random vector of interest. For the purpose of inference, a rank-based statistic is derived and its asymptotic behavior is stated. These new concepts are illustrated with both theoretical models and real data, showing that our methodology performs well in practice.

中文翻译：

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尾部依赖仪

非简并多元尾部依赖结构的所有特征都是功能性的和无穷大的。利用Hoeffding-Sobol分解的优势，我们得出了新的指标，以进行多变量极值分析中的依赖性强度测量和总结。尾部超集重要性系数提供了渐近依赖结构的成对排序。然后，我们定义尾部依赖图，该图在视觉上对目标随机向量的各个分量之间的极值依赖性进行排序。为了进行推断，导出了基于等级的统计量，并陈述了其渐近行为。这些新概念通过理论模型和实际数据进行了说明，表明我们的方法论在实践中表现良好。