On qualitative robustness of the Lotka--Nagaev estimator for the offspring mean of a supercritical Galton--Watson process

We show that the Lotka--Nagaev estimator for the mean of a supercritical Galton--Watson process is qualitatively robust on fairly large sets of offspring laws. As a by-product we obtain that the Lotka--Nagaev estimator is uniformly conditionally weakly consistent on these sets of offspring laws.