Minimum Hellinger distance estimation for supercritical Galton–Watson processes

This paper studies the asymptotic behavior of the minimum Hellinger distance estimator of the underlying parameter in a supercritical branching process whose offspring distribution is known to belong to a parametric family. This estimator is shown to be asymptotically normal, efficient at the true model and robust against gross errors. These extend the results of Beran (Ann. Statist. 5, 445–463 (1977)) from an i.i.d., continuous setup to a dependent, discrete setup.