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Closed-form maximum likelihood estimator for generalized linear models in the case of categorical explanatory variables: application to insurance loss modeling

Author

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  • Alexandre Brouste

    (Le Mans Université)

  • Christophe Dutang

    (Univ. Paris-Dauphine, Univ. PSL)

  • Tom Rohmer

    (Le Mans Université)

Abstract

Generalized linear models with categorical explanatory variables are considered and parameters of the model are estimated by an exact maximum likelihood method. The existence of a sequence of maximum likelihood estimators is discussed and considerations on possible link functions are proposed. A focus is then given on two particular positive distributions: the Pareto 1 distribution and the shifted log-normal distributions. Finally, the approach is illustrated on an actuarial dataset to model insurance losses.

Suggested Citation

  • Alexandre Brouste & Christophe Dutang & Tom Rohmer, 2020. "Closed-form maximum likelihood estimator for generalized linear models in the case of categorical explanatory variables: application to insurance loss modeling," Computational Statistics, Springer, vol. 35(2), pages 689-724, June.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:2:d:10.1007_s00180-019-00918-7
    DOI: 10.1007/s00180-019-00918-7
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    References listed on IDEAS

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    1. Stan Lipovetsky, 2015. "Analytical closed-form solution for binary logit regression by categorical predictors," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(1), pages 37-49, January.
    2. Ozkok, Erengul & Streftaris, George & Waters, Howard R. & Wilkie, A. David, 2012. "Bayesian modelling of the time delay between diagnosis and settlement for Critical Illness Insurance using a Burr generalised-linear-type model," Insurance: Mathematics and Economics, Elsevier, vol. 50(2), pages 266-279.
    3. Beirlant, Jan & Goegebeur, Yuri, 2003. "Regression with response distributions of Pareto-type," Computational Statistics & Data Analysis, Elsevier, vol. 42(4), pages 595-619, April.
    4. Beirlant, Jan & Goegebeur, Yuri & Verlaak, Robert & Vynckier, Petra, 1998. "Burr regression and portfolio segmentation," Insurance: Mathematics and Economics, Elsevier, vol. 23(3), pages 231-250, December.
    5. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
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    Cited by:

    1. Alexandre Brouste & Christophe Dutang & Tom Rohmer, 2022. "A Closed-form Alternative Estimator for GLM with Categorical Explanatory Variables," Post-Print hal-03689206, HAL.
    2. Christophe Dutang & Quentin Guibert, 2021. "An explicit split point procedure in model-based trees allowing for a quick fitting of GLM trees and GLM forests," Post-Print hal-03448250, HAL.

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