论文标题
极端的多元稀疏聚类
Multivariate sparse clustering for extremes
论文作者
论文摘要
确定发生极端事件的方向是多元极端价值分析的主要挑战。在本文中，我们使用Meyer和Wintenberger（2021）}引入的稀疏规则变化的概念来推断随机向量X的尾巴依赖性。这种方法依赖于欧几里得投影对单纯X的投影，这些投影比标准方法更好地表现出X尾巴的稀疏结构。我们基于严格方法的程序旨在捕获X的极端坐标集群。它还包括识别阈值，在该阈值之上，X所述的值被认为是极端的。我们提供了一种称为Muscle的有效且可扩展的算法，并将其应用于数值示例，以突出我们发现的相关性。最后，我们用财务回报数据来说明我们的方法。
Identifying directions where extreme events occur is a major challenge in multivariate extreme value analysis. In this paper, we use the concept of sparse regular variation introduced by Meyer and Wintenberger (2021)} to infer the tail dependence of a random vector X. This approach relies on the Euclidean projection onto the simplex which better exhibits the sparsity structure of the tail of X than the standard methods. Our procedure based on a rigorous methodology aims at capturing clusters of extremal coordinates of X. It also includes the identification of the threshold above which the values taken by X are considered as extreme. We provide an efficient and scalable algorithm called MUSCLE and apply it on numerical examples to highlight the relevance of our findings. Finally we illustrate our approach with financial return data.
