Abstract

Due to their flexibility, copulas have become a useful tool for modeling dependencies
in many statistical problems. In general, a copula function characterizes the average
dependence structure of random variables of interest. However, in the presence of covariates,
the copula need to be adjusted to better account for the dependence between the random variables.
This motivates the introduction of conditional copula in the literature. In this paper,
we propose a nonparametric kernel-type estimator for the bivariate conditional copula. This
estimator is derived from a mathematical representation of the bivariate conditional copula
via an integral of a trivariate copula density. We establish the asymptotic properties of this
estimator and propose a selection method for the bandwidth parameter. Numerical simulations
will be conducted to assess the performance of the proposed estimator, as well as
applications to real data sets.