Copula的参数与半参数估计方法的比较

Comparison of Parametric and Semiparametric Estimation Methods for Copula

本文主要是在极大似然法的基础上,研究Copula的参数和半参数方法的估计效果。通过随机模拟,比较各个估计量的偏差、均方误差和赤迟信息准则,得知两步极大似然参数估计方法受边际分布的影响较大。一旦边际分布拟合出现误差,该方法的稳健性会很差。一是估计出的Copula参数会有较大的偏差和均方误差,二是赤迟信息准则的结果显示,该方法会错误地指定Copula函数类。相比之下,半参数估计不受边际分布的影响,稳健性要好。因此在估计Copula参数,特别是无法确定边际分布函数类型时,应该用半参数方法而不是参数方法。

In this paper, we study the efficiency of parametric and semiparametric methods of estimating Copula by maximum likelihood method. Comparing the bias, mean square error and Akaike information criterion of all estimators by stochastic simulation, we obtain that the marginal distributions have much impact on parametric method such as two step maximum likelihood method. Once the goodness fit of the marginal distributions is not good enough, the robustness of this method is quite bad. Specifically, it is observed that the bias and mean square error of parameter estimators for Copula function are large. In addition the Akaike information criterion implies that two-steps maximum likelihood method may indicate wrong type of Copula function. By contrast, semiparametric method is not affected by the marginal distributions and has a robust estimator. Therefore, for estimating the parameters of Copula, we should use the semiparamertrie rather than parametric method when the marginal distributions can not be certainly determined.