Nonparametric estimation of copula functions for dependence modelling
Copulas are full measures of dependence among components of random vectors. Unlike the marginal and the joint distributions which are directly observable, a copula is a hidden dependence structure that couples the marginals and the joint distribution. This makes the task of proposing a parametric copula model non-trivial and is where a nonparametric estimator can play a significant role. In this paper, we investigate a kernel estimator which is mean square consistent everywhere in the support of the copula function. The kernel estimator is then used to formulate a goodness-of-fit test for parametric copula models.
This preprint was published as Song Xi Chen and Tzee-Ming Huang, "Nonparametric Estimation of Copula Functions for Dependence Modelling", Canadian Journal of Statistics (2009): 265-282, doi: 10.1002/cjs.5550350205