The conditional copula model arises when the dependence between random variables is influenced by another covariate. Despite its importance in modelling complex dependence structures, there are very few fully nonparametric approaches to estimate the conditional copula function. In the bivariate setting, the only nonparametric estimator for the conditional copula is based on Sklar's Theorem and proposed by Gijbels \textit{et al.} (2011). In this paper, we propose an alternative nonparametric approach %based on functional principal component analysis. We to construct an estimator for the bivariate conditional copula from the Karhunen-Lo\`eve representation of a suitably defined conditional copula process. We establish its consistency and weak convergence to a limit Gaussian process with explicit covariance function.

翻译：条件Copula模型适用于随机变量间的相依性受另一协变量影响的情形。尽管该模型在刻画复杂相依结构中具有重要作用，目前完全非参数的条件Copula函数估计方法仍极为有限。在二元变量设定下，唯一基于Sklar定理的非参数条件Copula估计量由Gijbels等人（2011）提出。本文提出一种基于函数主成分分析的非参数替代方法，通过适当定义的条件Copula过程的Karhunen-Loève表示来构建二元条件Copula估计量。我们证明了该估计量的一致性及其弱收敛于具有显式协方差函数的极限高斯过程。