In this paper, we estimate the sparse dependence structure in the tail region of a multivariate random vector, potentially of high dimension. The tail dependence is modeled via a graphical model for extremes embedded in the Hüsler-Reiss distribution. We propose the extreme graphical lasso procedure to estimate the sparsity in the tail dependence, similar to the Gaussian graphical lasso in high dimensional statistics. We prove its consistency in identifying the graph structure and estimating model parameters. The efficiency and accuracy of the proposed method are illustrated by simulations and real data examples.

翻译：本文估计了多元随机向量尾区域中的稀疏依赖结构，该向量可能具有高维特征。尾部依赖性通过嵌入Hüsler-Reiss分布的极值图模型进行建模。我们提出极值图套索方法，类似于高维统计学中的高斯图套索，以估计尾部依赖中的稀疏性。我们证明了该方法在识别图结构和估计模型参数方面的一致性。通过模拟实验和实际数据示例，验证了所提方法的有效性和准确性。