Selection of Mixed Copula Model via Penalized Likelihood
Selection of Mixed Copula Model via Penalized Likelihood
复制标题
通过惩罚似然选择混合Copula模型
DOI：
10.1080/01621459.2013.873366
复制
发表时间：
2014-06-01
影响因子：
3.7
通讯作者：
Wang, Xian
中科院分区：
文献类型：
--
作者：
Cai, Zongwu;Wang, Xian
如何为给定问题选择合适的Copula函数是Copula方法在应用中的一个基本问题。在这篇文章中，我们通过提出一种新的基于惩罚似然和收缩算子的联结选择方法来解决这个问题。该方法选择合适的Copula函数，同时估计相关参数。我们建立了惩罚似然估计的渐近性质，包括收敛速度、渐近正态和反常性质。特别地，当真系数参数可能在参数空间的边界上，而相依参数在参数空间的一个未知子集上时，我们证明了边界参数估计的极限分布是半正态的，未知参数的惩罚似然估计收敛到任意值。最后，通过蒙特卡罗模拟验证了该方法的有限样本性能，并将该方法用于研究金融股票市场的相关性结构和协变关系。
A fundamental issue of applying a copula method in applications is how to choose an appropriate copula function for a given problem. In this article we address this issue by proposing a new copula selection approach via penalized likelihood plus a shrinkage operator. The proposed method selects an appropriate copula function and estimates the related parameters simultaneously. We establish the asymptotic properties of the proposed penalized likelihood estimator, including the rate of convergence and asymptotic normality and abnormality. Particularly, when the true coefficient parameters may be on the boundary of the parameter space and the dependence parameters are in an unidentified subset of the parameter space, we show that the limiting distribution for boundary parameter estimator is half-normal and the penalized likelihood estimator for unidentified parameter converges to an arbitrary value. Finally, Monte Carlo simulation studies are carried out to illustrate the finite sample performance of the proposed approach and the proposed method is used to investigate the correlation structure and comovement of financial stock markets.