Simulation study on the offspring mean estimators in discrete time branching processes with migration

In the present work we consider two widely used definitions of a branching process with migration, related to the controlled branching processes framework, classical and multiple. We simulate the two processes with equal offspring and migration characteristics and estimate the offspring mean via the weighted conditional least squares estimators based on two sampling schemes – on the generation sizes only and the generation sizes and the migration components. We propose a robust modification of the second estimator in the case when several trajectories of the process are observed.