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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

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GLM-2018-final.pdf (860.0Kb)
Date
2019
Dewey
Probabilités et mathématiques appliquées
Sujet
Regression models; Heavy-tailed distributions; Explicit MLE; Insurance claim modeling
Journal issue
Computational Statistics
Volume
35
Publication date
2019
Article pages
689–724
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s00180-019-00918-7
Forthcoming
oui
URI
https://basepub.dauphine.fr/handle/123456789/19679
Collections
  • CEREMADE : Publications
Metadata
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Author
Brouste, Alexandre
90071 Laboratoire Manceau de Mathématiques [LMM]
Dutang, Christophe
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Rohmer, Tom
90071 Laboratoire Manceau de Mathématiques [LMM]
Type
Article accepté pour publication ou publié
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.

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