关键词: Copula, 随机模拟, 参数和半参数估计方法, 稳健性

Abstract: 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 semiparamertric rather than parametric method when the marginal distributions can not be certainly determined.

Key words: Copula, Stochastic Simulation, Parametric and Semiparametric Estimation Methods, Robustness