Parameter Estimation of Some Archimedean Copulas Based on Minimum Cramér-von-Mises Distance

The purpose of this paper is to introduce a new estimation method for estimating the Archimedean copula dependence parameter in the non-parametric setting. The estimation of the dependence parameter has been selected as the value that minimizes the Cramér-von-Mises distance which measures the distance between Empirical Bernstein Kendall distribution function and true Kendall distribution function. A Monte Carlo study is performed to measure the performance of the new estimator and compared to conventional estimation methods. In terms of estimation performance, simulation results show that the proposed Minumum Cramér-von-Mises estimation method has a good performance for low dependence and small sample size when compared with the other estimation methods. The new minimum distance estimation of the dependence parameter is applied to model the dependence of two real data sets as illustrations.