Probabilities of Concurrent Extremes
Probabilities of Concurrent Extremes
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DOI：
10.1080/01621459.2017.1356318
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发表时间：
2018-01-01
影响因子：
3.7
通讯作者：
Stoev, Stilian
中科院分区：
文献类型：
--
作者：
Dombry, Clement;Ribatet, Mathieu;Stoev, Stilian
空间极值的统计建模是近年来研究的一个活跃领域，其应用领域也在不断扩大。然而，现有的许多方法侧重于极端事件的规模，而不是其时间。为了解决这个问题，本文研究了极值并发的概念。假设在几个天气观测站测量日气温。我们说，如果记录的最高温度同时发生，也就是说，在同一天的所有站的极端并发。能够理解、量化和建模极值并发是很重要的。在一般条件下，我们证明了有限样本并发概率收敛于一个渐近量，即极值并发概率。使用Palm演算，我们建立了一般表达式的极值并发概率，通过最大稳定过程出现在极限的组件明智的最大值的样本。给出了各种最大稳定模型的极值并发概率的显式表达式，并介绍了几种估计量。特别地，我们证明了极大稳定向量的两两极值并发概率精确地等于Kendall的。评估的估计，从模拟和应用研究在美国的极端温度。结果表明，并发概率可以用来研究，例如，全球气候现象，如厄尔尼诺南方涛动（ENSO）或全球变暖的空间结构和极端的区域影响的影响。
The statistical modeling of spatial extremes has been an active area of recent research with a growing domain of applications. Much of the existing methodology, however, focuses on the magnitudes of extreme events rather than on their timing. To address this gap, this article investigates the notion of extremal concurrence. Suppose that daily temperatures are measured at several synoptic stations. We say that extremes are concurrent if record maximum temperatures occur simultaneously, that is, on the same day for all stations. It is important to be able to understand, quantify, and model extremal concurrence. Under general conditions, we show that the finite sample concurrence probability converges to an asymptotic quantity, deemed extremal concurrence probability. Using Palm calculus, we establish general expressions for the extremal concurrence probability through the max-stable process emerging in the limit of the component-wise maxima of the sample. Explicit forms of the extremal concurrence probabilities are obtained for various max-stable models and several estimators are introduced. In particular, we prove that the pairwise extremal concurrence probability for max-stable vectors is precisely equal to the Kendall's . The estimators are evaluated from simulations and applied to study temperature extremes in the United States. Results demonstrate that concurrence probability can be used to study, for example, the effect of global climate phenomena such as the El Nino Southern Oscillation (ENSO) or global warming on the spatial structure and areal impact of extremes.