An adjusted iterative algorithmic approach for maximum likelihood estimation of the pseudo-copula regression: P-MBP

Abstract

In this study, a pseudo-maximization by parts method is introduced by developing the maximization by parts algorithm for the parameter estimation of pseudo-copula regression models. Sub and main score equations are obtained from the pairwise log-likelihood function and solved by the proposed iterative algorithm. The pseudo-maximization by parts algorithm is an iterative algorithm to avoid having to calculate the second-order derivative of the full log-likelihood function as maximization by parts algorithm. Instead of the Gaussian copula function in maximization by parts algorithm, the pseudo-Gaussian copula function is included in the new algorithm. The mean square errors of the estimators found by the maximization by parts algorithm and the pseudo-maximization by parts algorithm were compared using real Turkish comprehensive insurance data taken from the Turkish Insurance Information and Monitoring Center for the year 2017 and it is notable that the proposed algorithm provided better results in terms of having lower errors.