Regression Models in Claims Analysis I: Theory

This paper considers the application of regression techniques to the analysis of claims data. Examples are given to indicate why, in certain circumstances, this might be preferable to traditional actuarial methods. The various errors of prediction which occur when loss reserves are estimated by regression are classified and discussed. Formal procedures are discussed for determining which of the available predictors will be entered into a regression, and the drawbacks of these procedures. Various approaches to the estimation of uncertainty associated with loss reserves estimated by regression are considered. The effect on regression techniques of outlying data points, and hence the subject of robust/resistant regression, is considered briefly.