Credibility in the Regression case Revisited (A Late Tribute to Charles A. Hachemeister)

Many authors have observed that Hachemeisters Regression Model for Credibility – if applied to simple linear regression – leads to unsatisfactory credibility matrices: they typically ‘mix up’ the regression parameters and in particular lead to regression lines that seem ‘out of range’ compared with both individual and collective regression lines. We propose to amend these shortcomings by an appropriate definition of the regression parameters: –intercept –slope Contrary to standard practice the intercept should however not be defined as the value at time zero but as the value of the regression line at the barycenter of time. With these definitions regression parameters which are uncorrected in the collective can be estimated separately by standard one dimensional credibility techniques. A similar convenient reparametrization can also be achieved in the general regression case. The good choice for the regression parameters is such as to turn the design matrix into an array with orthogonal columns.