Determining the dependence structure of multivariate extremes
Determining the dependence structure of multivariate extremes
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DOI：
10.1093/biomet/asaa018
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发表时间：
2018-09
期刊：
影响因子：
2.7
通讯作者：
Emma S. Simpson;J. Wadsworth;J. Tawn
中科院分区：
文献类型：
--
作者：
Emma S. Simpson;J. Wadsworth;J. Tawn
在多变量极值分析中，在选择合适的统计模型时，应考虑变量间极值相关性的性质。兴趣通常在于确定哪些变量子集可以同时取其最大值，而其他子集的顺序较小。我们的方法利用了非标准锥集合上隐藏的正则变化特性，并提供了一组新的指标，这些指标揭示了通过现有的依赖度量无法获得的极值依赖结构的各个方面。我们推导了这些指标的理论性质，通过一系列例子证明了它们的效用，并开发了推断方法，也估计了与每个锥体相关的极端质量的比例。我们将这些方法应用于英国的河流流量，估计不同站点子集同时较大的概率。
In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies in determining which subsets of variables can take their largest values simultaneously while the others are of smaller order. Our approach to this problem exploits hidden regular variation properties on a collection of nonstandard cones, and provides a new set of indices that reveal aspects of the extremal dependence structure not available through existing measures of dependence. We derive theoretical properties of these indices, demonstrate their utility through a series of examples, and develop methods of inference that also estimate the proportion of extremal mass associated with each cone. We apply the methods to river flows in the U.K., estimating the probabilities of different subsets of sites being large simultaneously.