Regular vine sequences permit the organisation of variables in a random vector along a sequence of trees. Regular vine models have become greatly popular in dependence modelling as a way to combine arbitrary bivariate copulas into higher-dimensional ones, offering flexibility, parsimony, and tractability. In this project, we use regular vine structures to decompose and construct the exponent measure density of a multivariate extreme value distribution, or, equivalently, the tail copula density. Although these densities pose theoretical challenges due to their infinite mass, their homogeneity property offers simplifications. The theory sheds new light on existing parametric families and facilitates the construction of new ones, called X-vines. Computations proceed via recursive formulas in terms of bivariate model components. We develop simulation algorithms for X-vine multivariate Pareto distributions as well as methods for parameter estimation and model selection on the basis of threshold exceedances. The methods are illustrated by Monte Carlo experiments and a case study on US flight delay data.

翻译：正则藤序列允许将随机向量中的变量沿树序列组织起来。正则藤模型在依赖关系建模中广受欢迎，它通过将任意二元copula组合为高维copula，提供了灵活性、简约性和可处理性。在本研究中，我们利用正则藤结构分解并构建多元极值分布的指数测度密度，或等价地，尾部copula密度。尽管这些密度因无穷质量而带来理论挑战，但它们的齐次性性质简化了问题。该理论为现有参数族提供了新的视角，并促进了新族（称为X-vine）的构建。计算通过基于二元模型组分的递归公式进行。我们开发了X-vine多元帕累托分布的模拟算法，以及基于阈值超出的参数估计和模型选择方法。通过蒙特卡洛实验和一项关于美国航班延误数据的案例研究，我们展示了这些方法的应用。