On the identification of a supercritical branching process [Sur l'identification d'un processus de branchement surcritique]

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 a??besta?? estimators for the mean, the variance, and the pair (mean, variance). The asymptotic independence for the standardized estimation errors is also established.