准椭圆Copula生成元的可辨识性与估计
Identifiability and estimation of meta-elliptical copula generators
摘要：
亚椭圆Copula常被用来描述随机向量的分量之间的依赖关系。它们由相关阵和映射$g$指定，称为密度生成器。虽然后者的相关阵可以很容易地估计从伪样本的观察，密度发生器是难以估计的，特别是当它不属于一个参数的家庭。我们给出了非参数化识别该生成元的充分条件。几个非参数估计的$g$，然后提出，M-估计，基于模拟的推理，或通过迭代程序中提供的R包ElliptCopulas。一些模拟说明了后一种方法的相关性。
英文摘要：
Meta-elliptical copulas are often proposed to model dependence between the components of a random vector. They are specified by a correlation matrix and a map $g$, called density generator. While the latter correlation matrix can easily be estimated from pseudo-samples of observations, the density generator is harder to estimate, especially when it does not belong to a parametric family. We give sufficient conditions to non-parametrically identify this generator. Several nonparametric estimators of $g$ are then proposed, by M-estimation, simulation-based inference, or by an iterative procedure available in the R package ElliptCopulas. Some simulations illustrate the relevance of the latter method.
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