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 loading structure may additionally exhibit sparsity, meaning that each component is influenced by only a small number of latent factors, which further enhances interpretability and scalability. Under mild structural assumptions, we establish identifiability of the model parameters and provide a constructive recovery procedure based on a margin-free tail pairwise dependence matrix, which also yields practical rank-based estimation methods. The framework combines naturally with marginal tail models and is particularly well suited to high-dimensional settings. We illustrate its applicability in a spatial wind energy application, where the latent factor structure enables tractable estimation of the risk that a large proportion of turbines simultaneously fall below their cut-in wind speed thresholds.

翻译：本文提出一类基于潜在线性因子结构的新型高维尾部相依模型，兼具可解释性。具体而言，可观测向量的极值相依性由低维潜在$K$因子模型驱动（其中$K \ll d$），从而实现了显式的维度约简。从几何角度看，这一特性体现在相应谱相依测度的支撑集上，其本征维度至多为$K-1$。载荷结构还可呈现稀疏性特征，即每个分量仅受少量潜在因子影响，这进一步增强了模型的可解释性与可扩展性。在温和的结构假设下，我们证明了模型参数的可识别性，并提出基于无边际尾部成对相依矩阵的构造性复原方法，该方法同时衍生出实用的秩估计方法。该框架可与边际尾部模型自然结合，尤其适用于高维场景。我们通过空间风能应用案例阐明其适用性：潜在因子结构使得能够对"大部分风机同时低于切入风速阈值"的风险进行可处理的估计。