一种用于全范围尾部依赖的新型可处理阿基米德 copula
A new tractable Archimedean copula for full-range tail dependence
- Northern Illinois University（北伊利诺伊大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种具有闭式密度函数的新型阿基米德 copula（FRA1），可捕获上下尾全范围尾部依赖，用于构建 vine 模型并应用于医疗支出数据，避免 pair-copula 选择。
AI中文摘要：
能够在下尾和上尾捕获全范围尾部依赖的参数化 copula 在许多应用中非常有用，包括作为 vine copula 模型中的 pair-copula 构建模块。然而，构造具有闭式密度函数的此类 copula 具有挑战性，这限制了它们在复杂建模场景中的实际适用性。据我们所知，所有现有的全范围尾部依赖 copula 都不具有闭式密度函数。在本文中，我们提出了一种新的阿基米德 copula 族，称为 I 型全范围阿基米德 copula（FRA1），它能够捕获两个尾部的全范围尾部依赖，并具有闭式密度函数。该 copula 有两个参数，一个控制下尾依赖的强度，另一个控制上尾依赖的强度。我们提供了该 copula 的依赖性质结果，并讨论了如何基于最大似然有效估计参数。我们仅使用 FRA1 copula 构建了一个 vine copula 模型，并证明该模型可以达到普通 vine copula 模型的相当性能，同时避免了 pair-copula 模型选择的需要。新的 copula 还应用于医疗支出小组调查的数据，表明 FRA1 vine 模型能够有效捕获医疗支出中多样化的时间和横截面依赖模式。最后，新的 copula 已在 R 包 CopulaOne 中实现，该包用于全范围尾部依赖 copula。
英文摘要：
Parametric copulas capable of capturing full-range tail dependence in both lower and upper tails are useful in many applications, including as pair-copula building blocks in vine copula models. However, it is challenging to create such copulas that have closed-form density functions, which limits their practical applicability in complex modeling scenarios. To the best of our knowledge, all existing full-range tail dependence copulas do not have closed-form density functions. In this paper, we propose a new Archimedean copula family, called the \emph{full-range Archimedean copula of type I} (FRA1), that captures full-range tail dependence in both tails and admits a closed-form density function. The copula has two parameters, one controlling the strength of dependence in the lower tail and the other controlling that in the upper tail. We provide results on dependence properties of the copula, and discuss how to effectively estimate the parameters based on maximum likelihood. We build a vine copula model only using the FRA1 copula, and demonstrate that the model can achieve comparable performance of an ordinary vine copula model while avoiding the need of pair-copula model selection. The new copula is also applied to data from the Medical Expenditure Panel Survey, demonstrating that an FRA1 vine model can effectively capture diverse temporal and cross-sectional dependence patterns in medical expenditures. Finally, the new copula is implemented in \texttt{CopulaOne}, an R package for full-range tail dependence copulas.
