Robust regression credibility: The influence function approach

In classical credibility theory we assume that the vector of claims Xj conditionally on Θj has independent components with identical means. However, this assumption is sometimes unrealistic. To relax this condition Hachemeister (Hachemeister, C.A., 1975. Credibility for regression models with application to trend. In: Kahn, P. (Ed.), Credibility, Theory and Applications. Academic Press, New York) introduced regressors. The presence of large claims can perturb the credibility premium estimation. The lack of robustness of regression credibility estimators, as well as the fairness of tariff evaluation, led to the development of this paper. Our proposal is to apply robust statistics to the regression credibility estimation by using the robust influence function approach of M-estimators.