A review on robust estimators applied to regression credibility

The lack of robustness of regression credibility estimators leads to the development of this paper. The appearance of outlier events (including large claims–catastrophic events) can offset the result of the ordinary least squares regression technique and perturb the credibility premium estimation. Our proposal is to apply robust statistical procedures to the regression credibility estimation, which are insensitive to the occurrence of outlier events in the data. A review of robust estimators that appeared in the literature is provided, including robust estimators that simultaneously attain maximum breakdown point and full asymptotic efficiency under normal errors. These estimators are the following: L1-estimators, M-estimators, GM-estimators, LMS-estimators, LTS-estimators, S-estimators, MM-estimators and robust REWLS-estimators. Applications of these estimators to regression credibility with two data sets are also presented herein.