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December 2005 Identification of multitype branching processes
F. Maaouia, A. Touati
Ann. Statist. 33(6): 2655-2694 (December 2005). DOI: 10.1214/009053605000000561

Abstract

We solve the problem of constructing an asymptotic global confidence region for the means and the covariance matrices of the reproduction distributions involved in a supercritical multitype branching process. Our approach is based on a central limit theorem associated with a quadratic law of large numbers performed by the maximum likelihood or the multidimensional Lotka–Nagaev estimator of the reproduction law means. The extension of this approach to the least squares estimator of the mean matrix is also briefly discussed.

On résout le problème de construction d’une région de confiance asymptotique et globale pour les moyennes et les matrices de covariance des lois de reproduction d’un processus de branchement multitype et supercritique. Notre approche est bas ée sur un théorème de limite centrale associé à une loi forte quadratique vérifiée par l’estimateur du maximum de vraisemblance ou l’estimateur multidimensionnel de Lotka–Nagaev des moyennes des lois de reproduction. L’extension de cette approche à l’estimateur des moindres carrés de la matrice des moyennes est aussi brièvement commentée.

Citation

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F. Maaouia. A. Touati. "Identification of multitype branching processes." Ann. Statist. 33 (6) 2655 - 2694, December 2005. https://doi.org/10.1214/009053605000000561

Information

Published: December 2005
First available in Project Euclid: 17 February 2006

zbMATH: 1099.62096
MathSciNet: MR2253098
Digital Object Identifier: 10.1214/009053605000000561

Subjects:
Primary: 60F05 , 60F15 , 60J80

Keywords: central limit theorem , Law of the iterated logarithm , least squares estimator , maximum likelihood estimator , multidimensional Lotka–Nagaev estimator , multitype branching process , quadratic strong law of large numbers

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 6 • December 2005
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