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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

Brouste, Alexandre; Dutang, Christophe; Rohmer, Tom (2019), Closed-form maximum likelihood estimator for generalized linear models in the case of categorical explanatory variables: application to insurance loss modeling, Computational Statistics, 35, p. 689–724. 10.1007/s00180-019-00918-7

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Type
Article accepté pour publication ou publié
Date
2019
Nom de la revue
Computational Statistics
Volume
35
Éditeur
Springer
Pages
689–724
Identifiant publication
Métadonnées
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Auteur(s)
Brouste, Alexandre cc
Laboratoire Manceau de Mathématiques [LMM]
Dutang, Christophe cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Rohmer, Tom
Laboratoire Manceau de Mathématiques [LMM]
Résumé (EN)
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.
Mots-clés
Regression models; Heavy-tailed distributions; Explicit MLE; Insurance claim modeling