A goodness-of-fit test based on Bezier curve estimation of Kendall distribution

In this study, we propose an estimation method for the Archimedean family of the copula in a nonparametric setting. A Bezier curve approach based on Bernstein polynomials is used to estimate the Kendall distribution function. Also, a new goodness-of-fit test based on Cramer-von Mises statistic is proposed using the Bezier curve estimator. A Monte Carlo study is also conducted to measure the performance of the proposed estimator and goodness-of-fit test. Two real data examples are also given. The simulation study and real data applications show that the Bezier curve estimator leads to satisfactory estimates of underlying copula and also has better results compared with the estimators based on empirical and Bernstein methods.