Non-Parametric Estimation Techniques of Factor Copula Model using Proxies

Abstract: 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.