A flexible parameter estimation method for the Farlie-Gumbel-Morgenstern copula: a simulation study

This research presents a minimum distance method based on the Bernstein empirical copula process for estimating the dependence parameter of the Farlie-Gumbel-Morgenstein copula. Also, this study examines its performance through a comprehensive Monte Carlo simulation study. The findings in this paper demonstrate that selecting the optimal degree of the Bernstein empirical copula has a significant impact on the performance of the new estimation method. The proposed estimator achieves optimal performance in terms of mean squared error (MSE) for the parameter range (Formula presented.) in small sample sizes, while outside this range, its performance varies depending on the degree of the Bernstein empirical copula. Finally, we apply the new method to real data for illustrative purposes.