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通过潜在线性因子模型降低多元极值的维度AI 解读

We propose a new and interpretable class of high-dimensional tail dependence models based on latent linear factor structures. Specifically, extremal dependence of an observable vector is assumed to be driven by a lower-dimensional latent $K$-factor model, where $K \ll d$, thereby inducing an explicit form of dimension reduction. Geometrically, this is reflected in the support of the associated spectral dependence measure, whose intrinsic dimension is at most $K-1$. The…

尾部依赖的结构化线性因子模型AI 解读

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…

利用模型聚类估计具有离散谱测度的最大稳定随机向量AI 解读

This study introduces a novel estimation method for the entries and structure of a matrix $A$ in the linear factor model $\mathbf{X} = A\textbf{Z} + \textbf{E}$. This is applied to an observable vector $\mathbf{X} \in \mathbb{R}^d$ with $\textbf{Z} \in \mathbb{R}^K$, a vector composed of independently regularly varying random variables, and lighter tail noise $\textbf{E} \in \mathbb{R}^d$. The spectral measure of the regularly varying random vector $\mathbf{X}$ is…