A longitudinal data analysis interpretation of credibility models

Insurance: Mathematics and Economics

Volumn 24, Issue 3, 1999, Pages 229-247

  Frees, Edward W ^a   Young, Virginia R ^a   Luo, Yu ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

Mixed linear models; Panel data models; Premium rating

Indexed keywords

EID: 0242343430     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6687(98)00055-9     Document Type: Article

References (41)

1. Baltagi, B.H., 1995. Econometric Analysis of Panel Data. Wiley, New York.
2. Bühlmann H. Experience rating and credibility. ASTIN Bulletin. 4:1967;199-207.
3. Bühlmann H., Gisler A. Credibility in the regression case revisited. ASTIN Bulletin. 27:1997;83-98.
4. Bühlmann H., Straub E. Glaubwürdigkeit für Schadensätze. Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker. 70:1970;111-133.
5. Corbeil R.R., Searle S.R. Restricted maximum likelihood (REML) estimation of variance components in the mixed model. Technometrics. 18:1976;31-38.
6. Corbeil R.R., Searle S.R. A comparison of variance components estimators. Biometrics. 32:1976;779-791.
7. Dannenburg D.R. Some results on the estimation of the credibility factor in the classical Bühlmann model. Insurance: Mathematics & Economics. 14:1994;39-50.
8. Dannenburg, D.R., Kaas, R., Goovaerts, M.J., 1996. Practical Actuarial Credibility Models. Institute of Actuarial Science and Econometrics, University of Amsterdam, Amsterdam, The Netherlands.
9. De Vylder F. Practical credibility theory with emphasis on optimal parameter estimation. ASTIN Bulletin. 12:1981;115-131.
10. Diggle, P.J., Liang, K.-Y., Zeger, S.L., 1994. Analysis of Longitudinal Data. Clarendon Press, Oxford.
11. Frees, E. W., Young, V.R., Luo, Y., 1998. Credibility ratemaking using longitudinal data models, working paper, University of Wisconsin-Madison.
12. Goldberger A.S. Best linear unbiased prediction in the generalized linear regression model. Journal of the American Statistical Association. 57:1962;369-375.
13. Goovaerts, M. J., Hoogstad, W., 1987. Credibility Theory, Surveys of Actuarial Studies. Nationale-Nederlanden N. V., Rotterdam.
14. Graybill, F.A., 1969. Matrices with Applications in Statistics, 2nd ed. Wadsworth, Belmont, California.
15. Hachemeister, C.A., 1975. Credibility for regression models with applications to trend. In: Kahn, P.M. (Ed.), Credibility: Theory and Applications. Academic Press, New York, pp. 129-163.
16. Hand, D.J., Crowder, M.J., 1996. Practical Longitudinal Data Analysis. Chapman-Hall, London.
17. Harville D.A. Bayesian inference for variance components using only error contrasts. Biometrika. 61:1974;383-385.
18. Harville D.A. Maximum likelihood approaches to variance component estimation and to related problems, with discussion. Journal of the American Statistical Association. 72:1977;320-340.
19. Harville D.A. Decomposition of prediction error. Journal of the American Statistical Association. 80:1985;132-138.
20. Henderson, C.R., 1973. Sire evaluation and genetic trends, in Proceedings of the Animal Breeding and Genetics Symposium in Honor of Dr. Jay L. Lush, 10-41. Amer. Soc. Animal Sci.-Amer. Dairy Sci. Assn. Poultry Sci. Assn., Champaign, IL.
21. Hsiao, C., 1986. Analysis of Panel Data. Cambridge University Press, Cambridge.
22. Jewell, W.S., 1975. The use of collateral data in credibility theory: A hierarchical model, Giornale dell'Istituto Italiano degli Attuari, 38, 1-16. (Also, Research Memorandum 75-24 of the International Institute for Applied Systems Analysis, Laxenburg, Austria.).
23. Kaas, R., Dannenburg, D., Goovaerts, M., 1997. Exact credibility for weighted observations, ASTIN Bulletin 27, 287-296.
24. Klugman, S., 1992. Bayesian Statistics in Actuarial Science. Kluwer, Boston.
25. Klugman, S., Panjer, H., Willmot, G., 1998. Loss Models: From Data to Decisions. Wiley, New York.
26. Ledolter J., Klugman S., Lee C.-S. Credibility models with time-varying trend components. ASTIN Bulletin. 21:1991;73-91.
27. Lee, Y., Nelder, J.A., 1996. Hierarchical generalized linear models. J. R. Stat. Soc., Series B 58, 619-678.
28. Lehmann, E., 1991. Theory of Point Estimation. Wadsworth & Brooks/Cole, Pacific Grove, CA.
29. Mátyás, L., Sevestre, P. (Eds.), 1996. The Econometrics of Panel Data. Kluwer, Dordrecht.
30. McCullagh, P., Nelder, J., 1989. Generalized Linear Models, 2nd ed. Chapman and Hall, London.
31. Nelder J.A., Verrall R.J. Credibility theory and generalized linear models. ASTIN Bulletin. 27:1997;71-82.
32. Norberg R. Empirical Bayes credibility. Scandinavian Actuarial Journal. 1980:1980;177-194.
33. Norberg R. On optimal parameter estimation in credibility. Insurance: Mathematics & Economics. 1:1982;73-89.
34. Norberg, R., 1986. Hierarchical credibility: Analysis of a random effect linear model with nested classification, Scandinavian Actuarial Journal, 204-222.
35. Patterson H.D., Thompson R. Recovery of inter-block information when block sizes are unequal. Biometrika. 58:1971;545-554.
36. Potthoff, R.F., Roy, S.N., 1964. A generalized multivariate analysis of variance model useful especially for growth curve problems. Biometrika, 51, 313-326.
37. Rao C.R. Estimation of variance and covariance components in linear models. Journal of the American Statistical Association. 67:1970;112-115.
38. Robinson G.K. That BLUP is a good thing: The estimation of random effects, with discussion. Statistical Science. 6:1991;15-51.
39. Swallow W.H., Searle S.R. Minimum variance quadratic unbiased estimation (MIVQUE) of variance components. Technometrics. 20:1978;265-272.
40. Swamy P.A.V.B. Efficient inference in a random coefficient regression model. Econometrica. 38:1970;311-323.
41. Wolfinger, R., Tobias, R., Sall, J., 1994. Computing Gaussian likelihoods and their derivatives for general linear mixed models. SIAM Journal of Scientific Computing 15 (6) 1294-1310.