论文标题
对葡萄藤的尾巴依赖性的几何研究
A geometric investigation into the tail dependence of vine copulas
论文作者
论文摘要
葡萄藤是一种多变量依赖模型，由根据特定的基础图形结构组合的双变量Copulas组成。它们在中等和高维度的灵活性和实用性导致了葡萄藤的普及，但对其极端特性的关注相对较少。为了解决这个问题，我们介绍了一些研究最广泛的葡萄藤类别的尾巴依赖性属性。我们将研究重点放在尾部依赖的系数和样品云的渐近形状上，我们使用Nolde（2014）的几何方法来计算这些系数。我们通过为由渐近依赖和渐近独立的双变量鸡蛋素构建的三变藤葡萄卵形的结果提供新的见解，重点是双变量极端价值和反转极值Copulas，并提供了针对物流和倒置的逻辑示例提供的其他细节。我们还为一类高维葡萄藤的新理论提出了新的理论，这些葡萄藤由双变量倒置的极值Copulas构建。
Vine copulas are a type of multivariate dependence model, composed of a collection of bivariate copulas that are combined according to a specific underlying graphical structure. Their flexibility and practicality in moderate and high dimensions have contributed to the popularity of vine copulas, but relatively little attention has been paid to their extremal properties. To address this issue, we present results on the tail dependence properties of some of the most widely studied vine copula classes. We focus our study on the coefficient of tail dependence and the asymptotic shape of the sample cloud, which we calculate using the geometric approach of Nolde (2014). We offer new insights by presenting results for trivariate vine copulas constructed from asymptotically dependent and asymptotically independent bivariate copulas, focusing on bivariate extreme value and inverted extreme value copulas, with additional detail provided for logistic and inverted logistic examples. We also present new theory for a class of higher dimensional vine copulas, constructed from bivariate inverted extreme value copulas.
