Parametric factor copula models typically work well in modeling multivariate dependencies due to their flexibility and ability to capture complex dependency structures. However, accurately estimating the linking copulas within these mod- els remains challenging, especially when working with high-dimensional data. This paper proposes a novel approach for estimating linking copulas based on a non-parametric kernel estimator. Unlike conventional parametric methods, our approach utilizes the flexibility of kernel density estimation to capture the un- derlying dependencies more accurately, particularly in scenarios where the un- derlying copula structure is complex or unknown. We show that the proposed estimator is consistent under mild conditions and demonstrate its effectiveness through extensive simulation studies. Our findings suggest that the proposed approach offers a promising avenue for modeling multivariate dependencies, par- ticularly in applications requiring robust and efficient estimation of copula-based models.

翻译：参数化因子Copula模型因其灵活性和捕捉复杂依赖结构的能力，通常在多元依赖建模中表现良好。然而，准确估计这些模型中的连接Copula函数仍然具有挑战性，尤其是在处理高维数据时。本文提出了一种基于非参数核估计的连接Copula函数估计新方法。与传统参数化方法不同，我们的方法利用核密度估计的灵活性来更准确地捕捉潜在依赖关系，特别是在底层Copula结构复杂或未知的场景中。我们证明了所提出的估计量在温和条件下具有一致性，并通过大量模拟研究验证了其有效性。研究结果表明，所提出的方法为多元依赖建模提供了有前景的途径，特别是在需要稳健高效估计Copula模型的应用中。