Thumbnail

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

View/Open
Type
Article accepté pour publication ou publié
Date
2019
Journal name
Computational Statistics
Volume
35
Publisher
Springer
Pages
689–724
Publication identifier
Metadata
Show full item record
Author(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]
Abstract (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.
Subjects / Keywords
Regression models; Heavy-tailed distributions; Explicit MLE; Insurance claim modeling