标题： 结构化线性因子模型用于尾部依赖 显示英文标题

标题： Structured linear factor models for tail dependence

摘要： 描述一个$d$维随机向量$X$极端依赖性的常见对象是稳定尾部依赖函数$L$。 各种参数模型已经出现，其中一种流行的子类包括那些由具有重尾因子的线性和极大线性因子模型产生的稳定尾部依赖函数。 然后，稳定尾部依赖函数通过一个$d \times K$矩阵$A$进行参数化，其中$K$是因子的数量，而$A$可以被解释为因子载荷矩阵。 我们研究在对$A$的额外假设下对$L$的估计，该假设称为“纯变量假设”。 $K \in \{1, \dots, d\}$和$A \in [0, \infty)^{d \times K}$均被视为未知，这构成了一个非常规的参数空间，无法适应常见的估计框架。 我们提出了两种算法，可以估计$K$和$A$，并为这两种算法提供了有限样本保证。 备注中提到，这些保证允许维度$d$大于样本大小$n$的情况。结果通过数值实验进行说明。 显示英文摘要

摘要： A common object to describe the extremal dependence of a $d$-variate random vector $X$ is the stable tail dependence function $L$. Various parametric models have emerged, with a popular subclass consisting of those stable tail dependence functions that arise for linear and max-linear factor models with heavy tailed factors. The stable tail dependence function is then parameterized by a $d \times K$ matrix $A$, where $K$ is the number of factors and where $A$ can be interpreted as a factor loading matrix. We study estimation of $L$ under an additional assumption on $A$ called the `pure variable assumption'. Both $K \in \{1, \dots, d\}$ and $A \in [0, \infty)^{d \times K}$ are treated as unknown, which constitutes an unconventional parameter space that does not fit into common estimation frameworks. We suggest two algorithms that allow to estimate $K$ and $A$, and provide finite sample guarantees for both algorithms. Remarkably, the guarantees allow for the case where the dimension $d$ is larger than the sample size $n$. The results are illustrated with numerical experiments.