WEAK CONVERGENCE RESULTS FOR CONTROLLED BRANCHING PROCESSES: STATISTICAL APPLICATIONS

In this communication it is proved a fluctuation limit theorem for controlled branching processes. Under the conditions that the offspring and control means tend to be $\textit{critical}$, the obtained limit is a diffusion process. This result is applied to conclude that the standard parametric bootstrap weighted conditional least squares estimate for the offspring mean is asymptotically invalid in the critical case.