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

Alexandre Brouste (), Christophe Dutang () and Tom Rohmer ()
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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 - INP - PURPAN - Ecole d'Ingénieurs de Purpan - Toulouse INP - Institut National Polytechnique (Toulouse) - UT - Université de Toulouse - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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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.

Keywords: Regression models; explicit estimators; categorical explanatory variables; GLM; asymptotic distribution (search for similar items in EconPapers)
Date: 2022-06-07
New Economics Papers: this item is included in nep-ecm
Note: View the original document on HAL open archive server: https://hal.science/hal-03689206v1
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Published in Communications in Statistics - Simulation and Computation, inPress, pp.1-17. ⟨10.1080/03610918.2022.2076870⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03689206

DOI: 10.1080/03610918.2022.2076870

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