A credibility approach for combining likelihoods of generalized linear models

Generalized linear models (GLM) are a popular tool for the modelling of insurance claims data. Problems arise with the model tting if little statistical information is available. In case that related statistics are available, statistical inference can be improved with the help of the borrowing-strength principle. We present a credibility approach that combines the maximum likelihood estimators of individual canonical GLMs in a meta-analytic way to an improved credibility estimator. We follow the concept of linear empirical Bayes estimation, which reduces the necessary parametric assumptions to a minimum. The concept is illustrated by a simulation study and an application example from mortality modeling.