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Fitting mixed-effects models when data are left truncated

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  • Paulsen, Jostein
  • Lunde, Astrid
  • Skaug, Hans Julius

Abstract

Damage sizes, i.e. all damages occurring to a policy and not only those that are reported to an insurance company, are modelled as a linear mixed model. Only those damages that are larger than their deductibles are reported to the company, and this fact should be taken into account when analyzing such data. In statistical terms, the problem is to make inference in a linear mixed model with left truncated data. Estimation methods based on a Monte Carlo simulation of the likelihood are proposed, and extensive simulations to evaluate the quality of the methods are reported. The proposed methods are then used to analyze claimsizes for some marine insurance data, where shipowners represent random effects and technical data about the ships represent fixed effects.

Suggested Citation

  • Paulsen, Jostein & Lunde, Astrid & Skaug, Hans Julius, 2008. "Fitting mixed-effects models when data are left truncated," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 121-133, August.
    • Handle: RePEc:eee:insuma:v:43:y:2008:i:1:p:121-133
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    1. Frees, Edward W. & Young, Virginia R. & Luo, Yu, 1999. "A longitudinal data analysis interpretation of credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 229-247, May.
    2. Malka Gorfine & David M. Zucker & Li Hsu, 2006. "Prospective survival analysis with a general semiparametric shared frailty model: A pseudo full likelihood approach," Biometrika, Biometrika Trust, vol. 93(3), pages 735-741, September.
    3. Elias Ould-Saïd & Mohamed Lemdani, 2006. "Asymptotic Properties of a Nonparametric Regression Function Estimator with Randomly Truncated Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 357-378, June.
    4. Edward Frees & Virginia Young & Yu Luo, 2001. "Case Studies Using Panel Data Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(4), pages 24-42.
    5. Nelder, J.A. & Verrall, R.J., 1997. "Credibility Theory and Generalized Linear Models," ASTIN Bulletin, Cambridge University Press, vol. 27(1), pages 71-82, May.
    6. Antonio, Katrien & Beirlant, Jan, 2007. "Actuarial statistics with generalized linear mixed models," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 58-76, January.
    7. Katrien Antonio & Jan Beirlant & Tom Hoedemakers & Robert Verlaak, 2006. "Lognormal Mixed Models for Reported Claims Reserves," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(1), pages 30-48.
    8. Sun, Liuquan, 2006. "The strong law under a semiparametric model for truncated and censored data," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1550-1558, August.
    9. Hajivassiliou, Vassilis & McFadden, Daniel & Ruud, Paul, 1996. "Simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 85-134.
    10. Amemiya, Takeshi, 1984. "Tobit models: A survey," Journal of Econometrics, Elsevier, vol. 24(1-2), pages 3-61.
    11. Jewell, William S., 1974. "Credible Means are exact Bayesian for Exponential Families," ASTIN Bulletin, Cambridge University Press, vol. 8(1), pages 77-90, September.
    12. David Clayton, 2003. "Conditional likelihood inference under complex ascertainment using data augmentation," Biometrika, Biometrika Trust, vol. 90(4), pages 976-981, December.
    13. Vijverberg, Wim P. M., 1997. "Monte Carlo evaluation of multivariate normal probabilities," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 281-307.
    14. Maria Karlsson, 2006. "Estimators of Regression Parameters for Truncated and Censored Data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 63(3), pages 329-341, June.
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    Cited by:

    1. Jackson P. Lautier & Vladimir Pozdnyakov & Jun Yan, 2022. "Pricing Time-to-Event Contingent Cash Flows: A Discrete-Time Survival Analysis Approach," Papers 2201.04981, arXiv.org, revised Jan 2023.
    2. Karlsson, Maria & Lindmark, Anita, 2014. "truncSP: An R Package for Estimation of Semi-Parametric Truncated Linear Regression Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 57(i14).

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