Inference on Selecting Optimal Copula Function Based on the Tracking Interval with Application in Insurance

One of the important issues in order to model dependency structure between interested variables is finding the proper copula function. Extensive studies has been done based on some criterions. The previous methods of selecting copula functions when the sample size is too small is not satisfactory. Therefore, our method is based on tracking interval for the semi-parametric copula function which is obtained using expected Kullback-Leibler risk between the two proposed non-nested semi-parametric copula model. It can find optimal semi-paramteric copula between proposed copula functions in a good level of significance. At the end, efficiency and capability of the presented method for Insurance data using simulation has been shown.