Copula Parameter Estimation by Maximum-Likelihood and Minimum-Distance Estimators - A Simulation Study

The purpose of this paper is to present a comprehensive Monte Carlo simulation study on the performance of minimum-distance (MD) and maximum-likelihood (ML) estimators for bivariate parametric copulae. In particular, I consider Cramer-von-Mises-, Kolmogorov-Smirnov- and L1-variants of the CvM-statistic based on the empirical copula process, Kendall's dependence function and Rosenblatt's probability integral transform. The results presented in this paper show that regardless of the parametric form of the copula, the sample size or the location of the parameter, maximum-likelihood yields smaller estimation biases at less computational effort than any of the MD-estimators. The MD-estimators based on copula goodness-of-fit metrics, on the other hand, suffer from large biases especially when used for estimating the parameters of archimedean copulae. Moreover, the results show that the bias and efficiency of the minimum-distance estimators are strongly influenced by the location of the parameter. Conversely, the results for the maximum-likelihood estimator are relatively stable over the parameter interval of the respective parametric copula