Max-stable processes serve as the fundamental distributional family in extreme value theory. However, likelihood-based inference methods for max-stable processes still heavily rely on composite likelihoods, rendering them intractable in high dimensions due to their intractable densities. In this paper, we introduce a fast and efficient inference method for max-stable processes based on their angular densities for a class of max-stable processes whose angular densities do not put mass on the boundary space of the simplex. This class can also be used to construct r-Pareto processes. We demonstrate the efficiency of the proposed method through two new max-stable processes: the truncated extremal-t process and the skewed Brown-Resnick process. The skewed Brown-Resnick process contains the popular Brown-Resnick model as a special case and possesses nonstationary extremal dependence structures. The proposed method is shown to be computationally efficient and can be applied to large datasets. We showcase the new max-stable processes on simulated and real data.

翻译：极大稳定过程是极值理论中的基础分布族。然而，基于似然的极大稳定过程推断方法仍严重依赖复合似然，因其密度函数难以处理，导致高维情形下推断不可行。本文针对一类角密度不在单纯形边界空间上赋质量的极大稳定过程，基于其角密度提出一种快速高效的推断方法。此类过程也可用于构造r-Pareto过程。通过两个新的极大稳定过程——截断极值t过程与偏斜Brown-Resnick过程，我们验证了所提方法的有效性。偏斜Brown-Resnick过程以经典的Brown-Resnick模型为特例，且具有非平稳极值相依结构。所提方法被证明计算高效，可应用于大规模数据集。我们在模拟数据与真实数据上展示了新极大稳定过程的性能。