An integral part of carrying out statistical analysis for bivariate extreme events is characterising the tail dependence relationship between the two variables. For instance, we may be interested in identifying the presence of asymptotic dependence and/or in determining whether an individual variable can be large while the other is of smaller order. In the extreme value theory literature, various techniques are available to assess or model different aspects of tail dependence; currently, inference must be carried out separately for each of these, with the possibility of contradictory conclusions. Recent developments by Nolde and Wadsworth (2022) have established theoretical links between different characterisations of extremal dependence, through studying the limiting shape of an appropriately-scaled sample cloud. We exploit these results for inferential purposes, by first developing an estimator for the sample limit set and then using this to deduce self-consistent estimates for the extremal dependence properties of interest. In simulations, the limit set estimates are shown to be successful across a range of distributions, and the estimates of dependence features are individually competitive with existing estimation techniques, and jointly provide a major improvement. We apply the approach to a data set of sea wave heights at pairs of locations, where the estimates successfully capture changes in the limiting shape of the sample cloud as the distance between the locations increases, including the weakening extremal dependence that is expected in environmental applications.

翻译：对两变极端事件进行统计分析的一个组成部分是说明这两个变量之间的尾部依赖关系。例如,我们可能有兴趣确定是否存在无症状依赖性和(或)确定个别变数是否大,而另一变数的顺序较小。在极端价值理论文献中,有各种技术可用于评估或模拟尾部依赖性的不同方面;目前,必须分别对其中每个方面进行推断,并有可能得出相互矛盾的结论。诺尔德和瓦德斯沃思(2022年)最近的发展在极端依赖性的不同特点之间建立了理论联系,通过研究适当规模的采样云的限定形状。我们利用这些结果来推断性目的,首先为抽样限数开发一个估计器,然后利用这个估计器推断出对极端依赖性特性的自我一致估计。在模拟中,设定的估计数在分布范围各异,依赖性特征的估计数与现有估计技术具有个别竞争力,并共同提供重大改进。我们利用这些结果进行推断,首先为推断目的,先开发一个抽样限值,然后用一个估计标准,然后用这个估计值来推算出各种热度的深度位置,从而将缩小海底的深度测测测测测测测测测测为海的距离。