A Functional Principal Component Analysis Approach to Conditional Copula Estimation

TL;DR

This paper introduces a novel nonparametric estimator for the bivariate conditional copula using functional principal component analysis, providing theoretical guarantees of consistency and weak convergence.

Contribution

It proposes a new nonparametric approach based on functional PCA for estimating conditional copulas, extending beyond existing methods.

Findings

Estimator is consistent and converges weakly to a Gaussian process.

Provides explicit covariance function for the limiting distribution.

Advances nonparametric dependence modeling with theoretical validation.

Abstract

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.