Title: Measures of non-simplifyingness for conditional copulas and vines Show Chinese title

Title: 条件Copula和vines的非简化性度量

Abstract: In copula modeling, the simplifying assumption has recently been the object of much interest. Although it is very useful to reduce the computational burden, it remains far from obvious whether it is actually satisfied in practice. We propose a theoretical framework which aims at giving a precise meaning to the following question: how non-simplified or close to be simplified is a given conditional copula? For this, we propose a new framework centered at the notion of measure of non-constantness. Then we discuss generalizations of the simplifying assumption to the case where the conditional marginal distributions may not be continuous, and corresponding measures of non-simplifyingness in this case. The simplifying assumption is of particular importance for vine copula models, and we therefore propose a notion of measure of non-simplifyingness of a given copula for a particular vine structure, as well as different scores measuring how non-simplified such a vine decompositions would be for a general vine. Finally, we propose estimators for these measures of non-simplifyingness given an observed dataset. A small simulation study shows the performance of a few estimators of these measures of non-simplifyingness. Show Chinese abstract

Abstract: 在copula建模中，简化的假设最近引起了广泛关注。尽管它非常有助于减少计算负担，但在实践中是否真的满足仍然远非显而易见。我们提出一个理论框架，旨在明确以下问题的含义：给定的条件copula有多不简化或接近简化？为此，我们提出一个以“非恒定性度量”概念为中心的新框架。然后我们讨论了简化假设的推广情况，其中条件边缘分布可能不连续，并讨论了在这种情况下相应的非简化性度量。简化假设对于vine copula模型尤为重要，因此我们提出了针对特定vine结构的给定copula的非简化性度量，以及不同评分指标，用于衡量一般vine结构下这样的vine分解有多不简化。最后，我们提出了在观察到的数据集下这些非简化性度量的估计量。一个小的模拟研究展示了这些非简化性度量的一些估计量的表现。