A closed-form alternative estimator for GLM with categorical explanatory variables

Brouste, Alexandre; Dutang, Christophe; Rohmer, Tom

Brouste, Alexandre; Dutang, Christophe; Rohmer, Tom (2022), A closed-form alternative estimator for GLM with categorical explanatory variables, Communications in Statistics - Simulation and Computation, p. 1-17. 10.1080/03610918.2022.2076870

View/Open

article_univariateGLM_depot_Hal.pdf (494.3Kb)

Type

Article accepté pour publication ou publié

Date

2022

Journal name

Communications in Statistics - Simulation and Computation

Pages

1-17

Laboratoire Manceau de Mathématiques [LMM]
Dutang, Christophe

CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Rohmer, Tom
Génétique Physiologie et Systèmes d'Elevage [GenPhySE ]

Abstract (EN)

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.

Subjects / Keywords

Regression models; explicit estimators; categorical explanatory variables; GLM; asymptotic distribution