Modeling Spatial Processes with Unknown Extremal Dependence Class
Modeling Spatial Processes with Unknown Extremal Dependence Class
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DOI：
10.1080/01621459.2017.1411813
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发表时间：
2019-01-02
影响因子：
3.7
通讯作者：
Wadsworth, Jennifer L.
中科院分区：
文献类型：
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作者：
Huser, Raphael;Wadsworth, Jennifer L.
随着事件变得更加极端，许多环境过程表现出空间相关性的减弱。众所周知的极限模型，如极大稳定或广义帕累托过程，无法捕捉到这一点，这可能导致对表现出渐近独立性的模型的偏好。然而，减弱依赖并不自动意味着渐近独立，而且这个过程是否真正的渐近(In)依赖通常远不清楚。这种区别是关键，因为它可能对外推产生很大影响，即估计发生比观测到的事件更极端的事件的概率。在这项工作中，我们提出了一个单一的空间模型，它能够以一种简约的方式捕捉两种依赖类，并在两种情况之间平稳过渡。该模型涵盖了从渐近独立性到完全相依性的多种可能性，并允许在渐近相依性下削弱极值的相依性。由于封闭式边际，隐含系词的删失似然推断在中等维度上是可行的。该模型被应用于具有模糊真实极限依赖结构的海洋数据集。这篇文章的补充材料可以在网上找到。
Many environmental processes exhibit weakening spatial dependence as events become more extreme. Well-known limiting models, such as max-stable or generalized Pareto processes, cannot capture this, which can lead to a preference for models that exhibit a property known as asymptotic independence. However, weakening dependence does not automatically imply asymptotic independence, and whether the process is truly asymptotically (in)dependent is usually far from clear. The distinction is key as it can have a large impact upon extrapolation, that is, the estimated probabilities of events more extreme than those observed. In this work, we present a single spatial model that is able to capture both dependence classes in a parsimonious manner, and with a smooth transition between the two cases. The model covers a wide range of possibilities from asymptotic independence through to complete dependence, and permits weakening dependence of extremes even under asymptotic dependence. Censored likelihood-based inference for the implied copula is feasible in moderate dimensions due to closed-form margins. The model is applied to oceanographic datasets with ambiguous true limiting dependence structure. Supplementary materials for this article are available online.