Weighted conditional least square estimators for bisexual branching processes with immigration

摘要

The aim of this paper is to study some inferential problems arising from the class of bisexual Galton–Watson branching processes with immigration of females and males (BGWPI). Immigrants are assumed to be unobservable, and it is only possible to sample the number of females, males, and couples (mating units) in each generation. Under these conditions, weighted conditional least square estimators are proposed for the offspring and immigration mean vectors. Asymptotic properties of such estimators are investigated when the process is subcritical and supercritical, paying especial attention to their strong consistency and limit distributions. Weighted conditional least square estimators are also developed for the offspring and immigration variance vectors, and their asymptotic properties are studied. Some comments on the critical case are also given to possibly provide a unified estimation theory for BGWPI.