Closed-form maximum likelihood estimator for generalized linear models in the case of categorical explanatory variables: application to insurance loss modeling

• DOI: 10.1007/s00180-019-00918-7
• Publication Date: 2019-08-22T13:02:52Z
• Authors: Alexandre Brouste; Christophe Dutang; Tom Rohmer
• Keywords: 330; explicit MLE; Generalized linear model; Explicit MLE; heavy-tailed distributions; Regression models; 01 natural sciences; Probabilités et mathématiques appliquées; insurance claim modeling; Heavy-tailed distributions; 519; [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]; 0101 mathematics; Insurance claim modeling

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.