A seemingly unrelated regression model in a credibility framework

There are various formulations for the randomly varying behavior of regression coefficients, which can be applied to credibility estimation. In this paper two different credibility estimation models are proposed, the credibility model of seemingly unrelated regressions (SUR) with fixed coefficients and of SUR model with random coefficients. For each model, unbiased credibility estimators are established, asymptotic optimality is proved and an application to real data is presented.