论文标题
基于等级的估计在渐近依赖性和独立性下，并应用于空间极端
Rank-based Estimation under Asymptotic Dependence and Independence, with Applications to Spatial Extremes
论文作者
论文摘要
多元极端价值理论与建模几个随机变量的关节尾行行为有关。现有工作主要集中在渐近依赖性上，在一个变量之一中观察一个大价值的概率与同时观察所有变量中的大价值的顺序相同。但是，越来越多的证据表明，渐近独立性在现实世界应用中同样重要。后一种环境中的可用统计方法很少，理论上尚未得到很好的理解。我们重新审视非参数估计，并为参数模型引入基于等级的M估计量，这些模型在渐近依赖性和渐近独立性下同时起作用，而无需对两个制度应用的哪个进行先验知识。提出的估计量的渐近态性是在较弱的规律条件下建立的。我们进一步展示了如何利用双变量估计器以在空间尾部模型中获得参数估计器，并再次为我们的方法提供了彻底的理论理由。
Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the variables is of the same order as observing a large value in all variables simultaneously. However, there is growing evidence that asymptotic independence is equally important in real world applications. Available statistical methodology in the latter setting is scarce and not well understood theoretically. We revisit non-parametric estimation and introduce rank-based M-estimators for parametric models that simultaneously work under asymptotic dependence and asymptotic independence, without requiring prior knowledge on which of the two regimes applies. Asymptotic normality of the proposed estimators is established under weak regularity conditions. We further show how bivariate estimators can be leveraged to obtain parametric estimators in spatial tail models, and again provide a thorough theoretical justification for our approach.
