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Robust regression credibility: The influence function approach

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  • Pitselis, Georgios

Abstract

In classical credibility theory we assume that the vector of claims conditionally on has independent components with identical means. However, this assumption is sometimes unrealistic. To relax this condition Hachemeister (Hachemeister, C.A., 1975. Credibility for regression models with application to trend. In: Kahn, P. (Ed.), Credibility, Theory and Applications. Academic Press, New York) introduced regressors. The presence of large claims can perturb the credibility premium estimation. The lack of robustness of regression credibility estimators, as well as the fairness of tariff evaluation, led to the development of this paper. Our proposal is to apply robust statistics to the regression credibility estimation by using the robust influence function approach of M-estimators.

Suggested Citation

  • Pitselis, Georgios, 2008. "Robust regression credibility: The influence function approach," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 288-300, February.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:1:p:288-300
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    References listed on IDEAS

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    1. De Vylder, Fl., 1978. "Parameter Estimation in Credibility Theory," ASTIN Bulletin, Cambridge University Press, vol. 10(1), pages 99-112, May.
    2. Rousseeuw, P. & Daniels, B. & Leroy, A., 1984. "Applying robust regression to insurance," Insurance: Mathematics and Economics, Elsevier, vol. 3(1), pages 67-72, January.
    3. Gisler, Alois & Reinhard, Peter, 1993. "Robust Credibility1," ASTIN Bulletin, Cambridge University Press, vol. 23(1), pages 117-143, May.
    4. Bühlmann, H. & Gisler, A., 1997. "Credibility in the Regression case Revisited (A Late Tribute to Charles A. Hachemeister)," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 83-98, May.
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    Cited by:

    1. Pitselis, Georgios, 2020. "Multi-stage nested classification credibility quantile regression model," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 162-176.
    2. Pitselis, Georgios, 2013. "Pure robust versus robust portfolio unbiased—Credibility and asymptotic optimality," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 391-403.
    3. Agustin Hernandez Bastida & Emilio Gomez Deniz & Jose Maria Perez Sanchez, 2009. "Bayesian robustness of the compound Poisson distribution under bidimensional prior: an application to the collective risk model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(8), pages 853-869.
    4. Dornheim, Harald & Brazauskas, Vytaras, 2011. "Robust-efficient credibility models with heavy-tailed claims: A mixed linear models perspective," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 72-84, January.

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