论文标题
通过正交预测对Copulas和Copula密度的非参数估算
Nonparametric estimation of copulas and copula densities by orthogonal projections
论文作者
论文摘要
在本文中，我们研究了Copulas和copula密度的非参数估计量。我们首先将研究重点放在基于关节密度的多项式正交投影的密度库估计器上。然后推导一个新的copula估计器。研究了它的渐近特性：我们提供了一个大型功能类别，该类别在Minimax和Maxiset Sense中是最佳的，我们为平滑参数提出了一种方法选择。一项密集的模拟研究表明，我们将Copulas和Copula密度估计器的表现非常好，我们将其与大量竞争对手进行了比较。精算科学中的真正数据集说明了这种方法。
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.
