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

Published online by Cambridge University Press:  29 August 2014

H. Bühlmann  and
A. Gisler
H. Bühlmann*
Affiliation:
ETH Zurich
A. Gisler*
Affiliation:
Winterhur-Versicherungen
*
Mathematics Department, ETH Zurich, CH – 8092 Zurich
“Winterthur”, Swiss Insurance Co., P. O. Box 357, CH – 8401 Winterthur
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Abstract

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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.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 27 , Issue 1 , May 1997 , pp. 83 - 98
Copyright
Copyright © International Actuarial Association 1997

References

Hachemeister, C. (1975) Credibility for regression models with application to trend. Credibility: Theory and Applications, (e.d. Kahn, D.M.), 129–163 Academic Press, New York.Google Scholar
Dannenburg, D. (1996) Basic actuarial credibility models. PhD Thesis University of Amsterdam.Google Scholar
De Vylder, F. (1981) Regression model with scalar credibility weights. Mitteilungen Vereinigung Schweizerischer Versicherungsmathematiker, Heft 1, 27–39.Google Scholar
De Vylder, F. (1985) Non-linear regression in credibility theory. Insurance: Mathematics and Economics 4, 163–172.Google Scholar