Afrika Statistika

Sur les estimateurs du maximum de vraisemblance dans les modèles multiplicatifs de Poisson et binomiale négative

Luciene Diégane Gning and Daniel Pierre-Loti-Viaud

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Abstract

We are interested in the existence and uniqueness of maximum likelihood estimators of parameters in the two multiplicative regression models, with Poisson or negative binomial probability distributions. Following its work on the multiplicative Poisson model with two factors without repeated measures, Haberman gave a necessary and sufficient condition for existence and uniqueness of the maximum likelihood estimator of this model, furthermore, he provided an explicit expression of this estimator. In this paper, we propose a generalization of these results to a multiplicative Poisson model with repeated measures and more than two factors. We also show that the condition obtained is also a necessary and sufficient condition for the existence and uniqueness of the maximum likelihood estimator in the multiplicative negative binomial model with several factors, with or without repeated measures.

Article information

Source
Afr. Stat., Volume 5, Number 1 (2010), 297-305.

Dates
First available in Project Euclid: 1 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.as/1388545352

Mathematical Reviews number (MathSciNet)
MR2920307

Zentralblatt MATH identifier
1327.62393

Subjects
Primary: 34K20: Stability theory 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 91B30: Risk theory, insurance

Keywords
Modèles de risque Probabilités de ruine Systèmes de files d'attente Interaction théorie de risque et files d’attente Stabilité forte inégalités de stabilité

Citation

Gning, Luciene Diégane; Pierre-Loti-Viaud, Daniel. Sur les estimateurs du maximum de vraisemblance dans les modèles multiplicatifs de Poisson et binomiale négative. Afr. Stat. 5 (2010), no. 1, 297--305. https://projecteuclid.org/euclid.as/1388545352


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