In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies with 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 non-standard 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 value 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 UK river flows, estimating the probabilities of different subsets of sites being large simultaneously.

中文翻译：

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确定多元极值的依赖结构

在多元极值分析中，选择合适的统计模型时，应考虑变量之间极值依赖的性质。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。我们解决这个问题的方法利用了一组非标准锥体上隐藏的规则变化特性，并提供了一组新的指数，这些指数揭示了通过现有依赖度量无法获得的极值依赖结构的各个方面。我们推导出这些指数的理论特性，通过一系列例子证明它们的价值，并开发推断方法，也估计与每个锥体相关的极值质量的比例。我们将这些方法应用于英国河流流量，