Abstract: Copulas characterize the dependence among components of random vectors. Unlike marginal

and joint distributions, which are directly observable, the copula of a random vector is a hidden dependence

structure that links the joint distribution with its margins. Choosing a parametric copula model is thus a

nontrivial task but it can be facilitated by relying on a nonparametric estimator. Here the authors propose

a kernel estimator of the copula that is mean square consistent everywhere on the support. They determine

the bias and variance of this estimator. They also study the effects of kernel smoothing on copula estimation.

They then propose a smoothing bandwidth selection rule based on the derived bias and variance.

After confirming their theoretical findings through simulations, they use their kernel estimator to formulate