We consider a single-type supercritical or near-critical size-dependent branching process such that the offspring mean converges to a limit with a rate of convergence of order as the population size grows to ∞ and the variance may change at the rate , where and . The offspring mean depends on an unknown parameter that we estimate on the non-extinction set by using the conditional least squares method. We prove the strong consistency of the estimator of as under some general conditions on the asymptotic behavior of the process. We also give its asymptotic distribution for a certain class of size-dependent branching processes.
On considère un processus de branchement taille-dépendant unitype supercritique ou presque-critique tel que sa descendance moyenne converge vers une limite à une vitesse de l'ordre de lorsque l'effectif de la population tend vers l'infini et tel que sa variance évolue à la vitesse où et . La descendance moyenne dépend d'un paramètre inconnu que l'on estime sur l'ensemble de non-extinction du processus à l'aide de la méthode des moindres carrés conditionnels. On démontre la consistance forte de l'estimateur de quand sous des hypothèses générales concernant le comportement asymptotique du processus. On donne aussi sa distribution asymptotique pour une certaine classe de processus taille-dépendants.
Accepted:
Published online:
Nadia Lalam 1; Christine Jacob 2
@article{CRMATH_2004__339_9_663_0, author = {Nadia Lalam and Christine Jacob}, title = {Estimation of the offspring mean of a supercritical or near-critical size-dependent branching process}, journal = {Comptes Rendus. Math\'ematique}, pages = {663--666}, publisher = {Elsevier}, volume = {339}, number = {9}, year = {2004}, doi = {10.1016/j.crma.2004.09.001}, language = {en}, }
TY - JOUR AU - Nadia Lalam AU - Christine Jacob TI - Estimation of the offspring mean of a supercritical or near-critical size-dependent branching process JO - Comptes Rendus. Mathématique PY - 2004 SP - 663 EP - 666 VL - 339 IS - 9 PB - Elsevier DO - 10.1016/j.crma.2004.09.001 LA - en ID - CRMATH_2004__339_9_663_0 ER -
Nadia Lalam; Christine Jacob. Estimation of the offspring mean of a supercritical or near-critical size-dependent branching process. Comptes Rendus. Mathématique, Volume 339 (2004) no. 9, pp. 663-666. doi : 10.1016/j.crma.2004.09.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.09.001/
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