论文标题
有条件极端的标准化的一些好处
Some benefits of standardisation for conditional extremes
论文作者
论文摘要
极端价值方法与标准统计模型不同的关键方面是通过具有渐近理论来为用于推断的模型的性质提供理论上的理由。在多元极端，已经提出了许多不同的渐近理论，部分原因是缺乏具有矢量随机变量的订购特性。 Heffernan and Tawn（2004）开发的一类基于条件限制理论的多元模型已发展为极端，它开发了广泛的实际用法。 Heffernan和Resnick（2007）和Resnick and Zeber（2014）的进一步理论特征支持了这种方法的基础价值。但是，Drees和Janßen（2017）提供了许多结果的反例，这可能会破坏对这些统计方法的信任。在这里，我们表明，在Heffernan and Tawn（2004）框架中，该框架涉及边际标准化，以呈指数型衰减的尾部边缘分布，这些示例中的问题被消除了。
A key aspect where extreme values methods differ from standard statistical models is through having asymptotic theory to provide a theoretical justification for the nature of the models used for extrapolation. In multivariate extremes many different asymptotic theories have been proposed, partly as a consequence of the lack of ordering property with vector random variables. One class of multivariate models, based on conditional limit theory as one variable becomes extreme, developed by Heffernan and Tawn (2004), has developed wide practical usage. The underpinning value of this approach has been supported by further theoretical characterisations of the limiting relationships by Heffernan and Resnick (2007) and Resnick and Zeber (2014). However Drees and Janßen (2017) provided a number of counterexamples of their results, which potentially undermine the trust in these statistical methods. Here we show that in the Heffernan and Tawn (2004) framework, which involves marginal standardisation to a common exponentially decaying tailed marginal distribution, the problems in these examples are removed.
