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A Closed-form Alternative Estimator for GLM with Categorical Explanatory Variables

Author

Listed:
  • Alexandre Brouste

    (LMM - Laboratoire Manceau de Mathématiques - UM - Le Mans Université)

  • Christophe Dutang

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Tom Rohmer

    (GenPhySE - Génétique Physiologie et Systèmes d'Elevage - ENVT - Ecole Nationale Vétérinaire de Toulouse - Toulouse INP - Institut National Polytechnique (Toulouse) - UT - Université de Toulouse - ENSAT - École nationale supérieure agronomique de Toulouse - Toulouse INP - Institut National Polytechnique (Toulouse) - UT - Université de Toulouse - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

The parameters of generalized linear models (GLMs) are usually estimated by the maximum likelihood estimator (MLE) which is known to be asymptotically efficient. But the MLE is computed using a Newton-Raphson-type algorithm which is time-consuming for a large number of variables or modalities, or a large sample size. An alternative closed-form estimator is proposed in this paper in the case of categorical explanatory variables. Asymptotic properties of the alternative estimator is studied. The performances in terms of both computation time and asymptotic variance of the proposed estimator are compared with the MLE for a Gamma distributed GLM.

Suggested Citation

  • Alexandre Brouste & Christophe Dutang & Tom Rohmer, 2022. "A Closed-form Alternative Estimator for GLM with Categorical Explanatory Variables," Post-Print hal-03689206, HAL.
    • Handle: RePEc:hal:journl:hal-03689206
    DOI: 10.1080/03610918.2022.2076870
    Note: View the original document on HAL open archive server: https://hal.science/hal-03689206
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    References listed on IDEAS

    as
    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. Denuit, Michel & Hainaut, Donatien & Trufin, Julien, 2020. "Effective Statistical Learning Methods for Actuaries II : Tree-Based Methods and Extensions," LIDAM Reprints ISBA 2020035, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. 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.
    4. 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.
    5. Marley, A.A.J. & Islam, T. & Hawkins, G.E., 2016. "A formal and empirical comparison of two score measures for best–worst scaling," Journal of choice modelling, Elsevier, vol. 21(C), pages 15-24.
    6. Lipovetsky, Stan & Conklin, Michael, 2014. "Best-Worst Scaling in analytical closed-form solution," Journal of choice modelling, Elsevier, vol. 10(C), pages 60-68.
    Full references (including those not matched with items on IDEAS)

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    Keywords

    Regression models; explicit estimators; categorical explanatory variables; GLM; asymptotic distribution;
    All these keywords.

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