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.

翻译：在本文中,我们研究非参数的焦云和焦云密度估计值。 我们首先将研究的重点放在基于对联合密度的多元正方形投影的密度焦云估计值上。 然后推算出一个新的焦云估计值。 研究的是其无症状特性: 我们提供了一个大型功能类, 其构造在微量和最大化意义上是最佳的, 我们为平滑参数提出一个方法选择。 密集的模拟研究显示, 焦云和焦云密度估计值的极好性能, 我们将其与众多的竞争者小组进行比较。 精算科学中真实的数据集展示了这一方法。