This paper addresses important weaknesses in current methodology for the estimation of multivariate extreme event distributions. The estimation of the residual dependence index $\eta \in (0,1]$ is notoriously problematic. We introduce a flexible class of reduced-bias estimators for this parameter, designed to ameliorate the usual problems of threshold selection through a unified approach to the familiar margins standardisation. We derive the associated asymptotic properties. The efficacy of the proposed semi-parametric inference on $\eta$ stems from a hitherto neglected exponentially decaying term in the hidden regular variation characterisation. Simulation studies to assess the performance for finite samples over a range of standard copulas indicate an improved performance, relative to the existing standard methods such as the Hill estimator. Our leading application illustrates how asymptotic independence can be discerned from monsoon-related rainfall occurrences at different locations in Ghana. The considerations involved in extending this framework to feasible inference on the extreme value index attached to domains of attraction are briefly discussed.

翻译：本文针对当前多元极端事件分布估计方法中的重要缺陷展开研究。残差依赖指数 $\eta \in (0,1]$ 的估计是众所周知的难题。我们为此参数引入了一类灵活的降偏估计量，旨在通过一种对常见边缘分布标准化处理的统一方法，来缓解通常的阈值选择问题。我们推导了相关的渐近性质。所提出的关于 $\eta$ 的半参数推断的有效性，源于隐正则变差表征中一个迄今被忽略的指数衰减项。在一系列标准Copula上评估有限样本性能的模拟研究表明，相对于Hill估计量等现有标准方法，其性能有所提升。我们的主要应用说明了如何从加纳不同地点与季风相关的降雨事件中识别渐近独立性。本文简要讨论了将此框架扩展到对吸引域所附极值指数进行可行推断时需考虑的因素。