[On the identification of a supercritical branching process]
We unify, under a one parameter family, the most common estimators of the mean and the variance of the offspring distribution for a supercritical one-type branching process. We give the rate for the almost-sure convergence, and the asymptotic normality for each one of these estimators. We select, within this family, the “best” estimators for the mean, the variance, and the pair (mean, variance). The asymptotic independence for the standardized estimation errors is also established.
On unifie, dans une même famille, les estimateurs usuels de la moyenne et de la variance associés à la loi de reproduction d'un processus de branchement monotype et surcritique. On précise la vitesse de convergence presque-sûre, ainsi que la normalité asymptotique pour chacun de ces estimateurs. On sélectionne, dans cette famille, les « meilleurs » estimateurs de la moyenne, de la variance et du couple (moyenne, variance). L'indépendance asymptotique des erreurs d'estimation est aussi établie.
Accepted:
Published online:
@article{CRMATH_2009__347_5-6_321_0,
author = {Hamza, Ka{\"\i}s and Ma\^aouia, Fa{\"\i}za},
title = {Sur l'identification d'un processus de branchement surcritique},
journal = {Comptes Rendus. Math\'ematique},
pages = {321--325},
publisher = {Elsevier},
volume = {347},
number = {5-6},
year = {2009},
doi = {10.1016/j.crma.2009.01.007},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.01.007/}
}
TY - JOUR AU - Hamza, Kaïs AU - Maâouia, Faïza TI - Sur l'identification d'un processus de branchement surcritique JO - Comptes Rendus. Mathématique PY - 2009 SP - 321 EP - 325 VL - 347 IS - 5-6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.01.007/ DO - 10.1016/j.crma.2009.01.007 LA - fr ID - CRMATH_2009__347_5-6_321_0 ER -
%0 Journal Article %A Hamza, Kaïs %A Maâouia, Faïza %T Sur l'identification d'un processus de branchement surcritique %J Comptes Rendus. Mathématique %D 2009 %P 321-325 %V 347 %N 5-6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.01.007/ %R 10.1016/j.crma.2009.01.007 %G fr %F CRMATH_2009__347_5-6_321_0
Hamza, Kaïs; Maâouia, Faïza. Sur l'identification d'un processus de branchement surcritique. Comptes Rendus. Mathématique, Volume 347 (2009) no. 5-6, pp. 321-325. doi : 10.1016/j.crma.2009.01.007. http://www.numdam.org/articles/10.1016/j.crma.2009.01.007/
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