The Annals of Statistics

Identification of multitype branching processes

F. Maaouia and A. Touati

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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.

Article information

Source
Ann. Statist., Volume 33, Number 6 (2005), 2655-2694.

Dates
First available in Project Euclid: 17 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.aos/1140191669

Digital Object Identifier
doi:10.1214/009053605000000561

Mathematical Reviews number (MathSciNet)
MR2253098

Zentralblatt MATH identifier
1099.62096

Subjects
Primary: 60F05: Central limit and other weak theorems 60F15: Strong theorems 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

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

Citation

Maaouia, F.; Touati, A. Identification of multitype branching processes. Ann. Statist. 33 (2005), no. 6, 2655--2694. doi:10.1214/009053605000000561. https://projecteuclid.org/euclid.aos/1140191669


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