论文标题
通过矩阵完成对Hüsler-Reiss图形模型的统计推断
Statistical Inference for Hüsler-Reiss Graphical Models Through Matrix Completions
论文作者
论文摘要
多元极端事件的严重程度是由最大的边际观测之间的依赖性驱动的。 Hüsler-Reiss分布是这种极端依赖性的多功能模型，通常由变量图矩阵进行参数化。为了表示有条件的独立关系并获得稀疏的参数化，我们介绍了小说的Hüsler-Reiss Precision矩阵。与高斯情况类似，该矩阵自然而然地以Hüsler-Reiss Pareto分布的密度表示，并通过其零模式编码极端图形结构。对于给定的任意图，我们证明了部分指定的Hüsler-Reiss-Reiss Variogram矩阵的完成的存在和唯一性，以便其精度矩阵在图中的非编号上具有零。我们的理论使用边缘上参数的合适估计器提供了图形结构的Hüsler-Reiss分布的第一个一致估计器。如果图未知，则可以将我们的方法与最近的结构学习算法结合使用，以共同推断图形和相应的参数矩阵。基于我们的方法，我们提出了新的工具来推断稀疏的Hüsler-Reiss模型，并在美国的大型飞行延迟数据以及多瑙河河流流量数据上进行了说明。
The severity of multivariate extreme events is driven by the dependence between the largest marginal observations. The Hüsler-Reiss distribution is a versatile model for this extremal dependence, and it is usually parameterized by a variogram matrix. In order to represent conditional independence relations and obtain sparse parameterizations, we introduce the novel Hüsler-Reiss precision matrix. Similarly to the Gaussian case, this matrix appears naturally in density representations of the Hüsler-Reiss Pareto distribution and encodes the extremal graphical structure through its zero pattern. For a given, arbitrary graph we prove the existence and uniqueness of the completion of a partially specified Hüsler-Reiss variogram matrix so that its precision matrix has zeros on non-edges in the graph. Using suitable estimators for the parameters on the edges, our theory provides the first consistent estimator of graph structured Hüsler-Reiss distributions. If the graph is unknown, our method can be combined with recent structure learning algorithms to jointly infer the graph and the corresponding parameter matrix. Based on our methodology, we propose new tools for statistical inference of sparse Hüsler-Reiss models and illustrate them on large flight delay data in the U.S., as well as Danube river flow data.
