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Structural Parameter Estimation Using Generalized Estimating Equations for Regression Credibility Models

Published online by Cambridge University Press:  17 April 2015

Chi Ho Lo ,
Wing Kam Fung  and
Zhong Yi Zhu
Wing Kam Fung
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China, Tel.: +852 2859 1988, Fax: +852 2858 9041, E-mail: [email protected]
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Abstract

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A generalized estimating equations (GEE) approach is developed to estimate structural parameters of a regression credibility model with independent or moving average errors. A comprehensive account is given to illustrate how GEE estimators are worked out within an extended Hachemeister (1975) framework. Evidenced by results of simulation studies, the proposed GEE estimators appear to outperform those given by Hachemeister, and have led to a remarkable improvement in accuracy of the credibility estimators so constructed.

Keywords

Credibility theoryHachemeister modelgeneralized estimating equations (GEE)regression modelrandom effects models
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 37 , Issue 2 , November 2007 , pp. 323 - 343
Copyright
Copyright © ASTIN Bulletin 2007

References

Bühlmann, H. (1967) Experience rating and credibility. ASTIN Bulletin 4, 199–207.CrossRefGoogle Scholar
Bühlmann, H. and Straub, E. (1970) Glaubwürdigkeit für Schadensätze (Credibility for loss ratios). Bulletin of the Swiss Association of Actuaries 70(1), 111–133.Google Scholar
Bühlmann, H. and Gisler, A. (1997) Credibility in the regression case revisited. ASTIN Bulletin 27, 83–98.CrossRefGoogle Scholar
Bühlmann, H. and Gisler, A. (2005) A Course in Credibility Theory and its Applications. Springer: Heidelberg.Google Scholar
Bühlmann, P. and Bühlmann, H. (1999) Selection of credibility regression models. ASTIN Bulletin 29, 245–270.CrossRefGoogle Scholar
Cossette, H. and Luong, A. (2003) Generalized least squares estimators for covariance parameters for credibility regression models with moving average errors. Insurance: Mathematics and Economics 32, 281–293.Google Scholar
Dannenburg, D.R., Kaas, R. and Goovaerts, M.J. (1996) Practical Actuarial Credibility Models. Institute of Actuarial Science and Econometrics, University of Amsterdam, Amsterdam, the Netherlands.Google Scholar
Frees, E.W., Young, V.R. and Luo, Y. (1999) A longitudinal data analysis interpretation of credibility models. Insurance: Mathematics and Economics 24, 229–247.Google Scholar
Fuller, W. (1987) Measurement Error Models. Wiley, New York.CrossRefGoogle Scholar
Graham, A. (1981) Kronecker Products and Matrix Calculus: with Applications. Horwood, Chichester.Google Scholar
Hachemeister, C.A. (1975) Credibility for regression models with application to trend. In: Kahn, P.M. (Ed.), Credibility: Theory and Applications. Academic Press, New York, pp. 129–163.Google Scholar
Hardin, J.W. and Hilbe, J.M. (2001) Generalized Linear Models and Extensions. Stata Press, Texas.Google Scholar
Hardin, J.W. and Hilbe, J.M. (2003) Generalized Estimating Equations. Chapman and Hall, Boca Raton.Google Scholar
He, X., Fung, W.K. and Zhu, Z.Y. (2005) Robust estimation in generalized partial linear models for clustered data. Journal of the American Statistical Association 100, 1176–1184.CrossRefGoogle Scholar
Liang, K.Y. and Zeger, S.L. (1986) Longitudinal data analysis using generalized linear models. Biometrika 73, 13–22.CrossRefGoogle Scholar
Liang, K.Y., Zeger, S.L. and Qaqish, B. (1992) Multivariate regression analyses for categorical data. Journal of the Royal Statistical Society Series B, 54, 3–40.Google Scholar
Lo, C.H., Fung, W.K. and Zhu, Z.Y. (2006) Generalized estimating equations for variance and covariance parameters in credibility models. Insurance: Mathematics and Economics, 39, 99–113.Google Scholar
McCullagh, P. and Nelder, J. (1989) Generalized Linear Models. Chapman and Hall, London.CrossRefGoogle Scholar
Nelder, J.A. and Verrall, R.J. (1997) Credibility theory and generalized linear models. ASTIN Bulletin 27, 71–82.CrossRefGoogle Scholar
Norberg, R. (1980) Empirical Bayes credibility. Scandinavian Actuarial Journal, 177–194.CrossRefGoogle Scholar
Norberg, R. (1982) On optimal parameter estimation in credibility. Insurance: Mathematics and Economics 1, 73–89.Google Scholar
Norberg, R. (1986) Hierarchical credibility: analysis of a random effect linear model with nested classification. Scandinavian Actuarial Journal, 204–222.CrossRefGoogle Scholar
Prentice, R.L. and Zhao, L.P. (1991) Estimating equations for parameters in means and covariances of multivariate discrete and continuous responses. Biometrics 47, 825–839.CrossRefGoogle ScholarPubMed
Rao, C.R. (1975) Simultaneous estimation of parameters in different linear models and applications to biometric problems. Biometrics 31, 545–554.CrossRefGoogle Scholar
Sundt, B. (1987) Two credibility regression approaches for the classification of passenger cars in a multiplicative tariff. ASTIN Bulletin 17, 41–70.CrossRefGoogle Scholar
Zeger, S.L. and Liang, K.Y. (1986) Longitudinal data analysis for discrete and continuous outcomes. Biometrics 42, 121–130.CrossRefGoogle ScholarPubMed