元椭圆 copula 生成器的可识别性和估计,Journal of Multivariate Analysis

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元椭圆 copula 生成器的可识别性和估计
Journal of Multivariate Analysis ( IF 1.4 ) Pub Date : 2022-02-16 , DOI: 10.1016/j.jmva.2022.104962
A. Derumigny ₁ , J.-D. Fermanian ₂

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元椭圆 copulas 经常被提出来模拟随机向量的分量之间的依赖关系。它们由相关矩阵和映射指定 $G$ ，称为密度发生器。虽然后一个相关矩阵可以很容易地从观察的伪样本中估计出来，但密度生成器更难估计，尤其是当它不属于参数族时。我们给出了充分的条件来非参数地识别这个生成器。几个非参数估计量 $G$ 然后通过 M 估计、基于模拟的推理或通过R包ElliptCopulas中可用的迭代过程提出。一些模拟说明了后一种方法的相关性。

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Identifiability and estimation of meta-elliptical copula generators

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.

更新日期：2022-02-16

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