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Maaouia, F.; Touati, A.

Identification of multitype branching processes. (English) Zbl 1099.62096

Ann. Stat. 33, No. 6, 2655-2694 (2005).
Summary: 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.

Cited in 7 Documents

MSC:

62M05 Markov processes: estimation; hidden Markov models
60F15 Strong limit theorems
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60F05 Central limit and other weak theorems
62H12 Estimation in multivariate analysis
62F25 Parametric tolerance and confidence regions
62F12 Asymptotic properties of parametric estimators

Keywords:

maximum likelihood estimator; multidimensional Lotka-Nagaev estimator; least squares estimator; quadratic strong law of large numbers; law of the iterated logarithm
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References:

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