  In this paper we study nonparametric estimators of copulas and copula
densities. We first focus our study on a density copula estimator based on a
polynomial orthogonal projection of the joint density. A new copula estimator
is then deduced. Its asymptotic properties are studied: we provide a large
functional class for which this construction is optimal in the minimax and
maxiset sense and we propose a method selection for the smoothing parameter. An
intensive simulation study shows the very good performance of both copulas and
copula densities estimators which we compare to a large panel of competitors. A
real dataset in actuarial science illustrates this approach.
