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 Huesler-Reiss distribution (Engelke and Hitz, 2020). We propose the extreme graphical lasso procedure to estimate the sparsity in the tail dependence, similar to the Gaussian graphical lasso method 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 in simulated and real examples.

翻译：本文估计了高维多元随机向量尾部区域的稀疏依赖结构。尾部依赖性通过嵌入于Huesler-Reiss分布的极值图模型（Engelke and Hitz, 2020）进行建模。我们提出极值图LASSO方法以估计尾部依赖的稀疏性，类似于高维统计中的高斯图LASSO方法。我们证明了该方法在图结构识别及模型参数估计中的一致性。通过模拟与实际案例验证了所提方法的效率与准确性。