论文标题
通过限制集链接多元极端的表示形式
Linking representations for multivariate extremes via a limit set
论文作者
论文摘要
多元极端的研究以多元规则变异为主，尽管众所周知，这种方法不能在分量并不总是同时大的随机矢量之间提供足够的区别。已经提出了各种替代依赖度量和表示形式，其中最著名的是隐藏的规则变化和条件的极值模型。这些对极端依赖性的不同描述是通过考虑多元域的不同部分而引起的，尤其是探索一个变量的极端可能以不同速率增长到其他变量时会发生什么。到目前为止，这些替代表示来自不同的来源，它们之间的联系是有限的。在这项工作中，我们通过几何方法阐明了许多相关连接。特别是，显示出光尾边缘中缩放样品云的极限集的形状被证明提供了几种不同的极端依赖表示形式的描述。
The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously large. Various alternative dependence measures and representations have been proposed, with the most well-known being hidden regular variation and the conditional extreme value model. These varying depictions of extremal dependence arise through consideration of different parts of the multivariate domain, and particularly exploring what happens when extremes of one variable may grow at different rates to other variables. Thus far, these alternative representations have come from distinct sources and links between them are limited. In this work we elucidate many of the relevant connections through a geometrical approach. In particular, the shape of the limit set of scaled sample clouds in light-tailed margins is shown to provide a description of several different extremal dependence representations.
