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Vine Copula Based Modeling
Annual Review of Statistics and Its Application ( IF 7.4 ) Pub Date : 2022-03-07 , DOI: 10.1146/annurev-statistics-040220-101153
Claudia Czado 1 , Thomas Nagler 2
Affiliation  

With the availability of massive multivariate data comes a need to develop flexible multivariate distribution classes. The copula approach allows marginal models to be constructed for each variable separately and joined with a dependence structure characterized by a copula. The class of multivariate copulas was limited for a long time to elliptical (including the Gaussian and t-copula) and Archimedean families (such as Clayton and Gumbel copulas). Both classes are rather restrictive with regard to symmetry and tail dependence properties. The class of vine copulas overcomes these limitations by building a multivariate model using only bivariate building blocks. This gives rise to highly flexible models that still allow for computationally tractable estimation and model selection procedures. These features made vine copula models quite popular among applied researchers in numerous areas of science. This article reviews the basic ideas underlying these models, presents estimation and model selection approaches, and discusses current developments and future directions.

中文翻译:


基于 Vine Copula 的建模

随着大量多元数据的可用性,需要开发灵活的多元分布类别。copula 方法允许为每个变量分别构建边际模型,并与以 copula 为特征的依赖结构相结合。多元 copula 的类长期以来被限制在椭圆(包括 Gaussian 和t-copula)和阿基米德家族(例如 Clayton 和 Gumbel copulas)。这两个类别在对称性和尾依赖属性方面都相当严格。vine copulas 类通过仅使用双变量构建块构建多变量模型来克服这些限制。这产生了高度灵活的模型,这些模型仍然允许计算上易于处理的估计和模型选择过程。这些特征使藤系连接模型在众多科学领域的应用研究人员中非常流行。本文回顾了这些模型的基本思想,介绍了估计和模型选择方法,并讨论了当前的发展和未来的方向。

更新日期:2022-03-07
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