Estimation of the Offspring and Immigration Mean Vectors for Bisexual Branching Processes with Immigration of Females and Males

2000 Mathematics Subject Classification: 60J80, 62M05.

This paper concerns with the bisexual branching model with immigration of females and males in each generation introduced in [4]. For this model the problem of estimating the offspring and immigration mean vectors is dealt. The estimation is considered in two sample situations, depending on the ability to observe the number of female and male immigrants or the impossibility to do it. The asymptotic properties of the proposed estimators are investigated in the supercritical case. The behaviour of the estimators is illustrated through a simulated example.

Research supported by the Ministerio de Ciencia e Innovacion and the FEDER through the Plan Nacional de Investigacion Cientıfica, Desarrollo e Innovacion Tecnologica, grant MTM2009-13248.