Estimation and Robustness of Linear Mixed Models in Credibility Context

In this paper, linear mixed models are employed for estimation of structural parameters in credibility context. In particular, Hachemeister’s model and Dannenburg’s crossed classification model are considered. Maximum likelihood (ML) and restricted maximum likelihood (REML) methods are developed to estimate the variance and covariance parameters. These estimators are compared with the classical Hachemeister’s and the Dannenburg’s estimators by simulation. The robustness properties of the ML and REML methods are also investigated. In the simulation studies, we have tested the performance of ML, REML, and the classical estimation approaches when the error terms are normally distributed and lognormally distributed. It is noticed that the proposed ML and REML approaches have clear advantages over the classical estimation approaches. The mean-squared errors of the proposed estimators can be a few hundred times smaller than those of classical estimators.