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Robust Methods for Credibility

Published online by Cambridge University Press:  29 August 2014

Hans R. Künsch
Hans R. Künsch*
Affiliation:
ETH, Zürich, Switzerland
*
Seminar für Statistik, ETH-Zentrum, CH-8092 Zürich, Switzerland
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Abstract

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Excess claims lead to an unsatisfactory behavior of standard linear credibility estimators. We suggest in this paper to use robust methods in order to obtain better estimators. Our first proposal is the linear credibility estimator with the claims replaced by a robust M-estimator of scale calculed from the claims. This corresponds to a truncation of the claims with a truncation point depending on the data and different for each contract. We discuss the properties of the robust M-estimator and present several examples. In order to improve the performance for a very small number of years, we propose a second estimator, which incorporates information from other claims into the M-estimator.

Keywords

Robust statisticscredibilitybig claimsiM/i-estimatorsinfluence function
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 22 , Issue 1 , May 1992 , pp. 33 - 49
Copyright
Copyright © International Actuarial Association 1992

References

REFERENCES

Efron, B. (1982) The Jackknife, lire Bootstrap and Other Resampling Plans. CBMS Regional Conference Series 38. SIAM Philadelphia.CrossRefGoogle Scholar
Gisler, A. (1980a) Optimales Stutzen von Beobachtungen im Credibility Modell. Ph. D. thesis, ETH Zürich, Nr. 6556.Google Scholar
Gisler, A. (1980b) Optimum trimming of data in the credibility model. Mitteilungen Ver. Schweiz., Vers. math. 80, 313–326.Google Scholar
Gisler, A. and Reinhard, P. (1990) Robust Credibility. Paper presented at the XXIIth Astin Colloquium, Montreux.Google Scholar
Hampel, F. R., Ronchetti, E. M., Rousseeuw, P.J. and Stahel, W.A. (1986) Robust Statistics: The Approach Based on Influence Functions. Wiley, New York.Google Scholar
Huber, P. (1981) Robust Statistics. Wiley, New York.CrossRefGoogle Scholar