Asymptotic behavior of CLS estimators for $2$-type doubly symmetric critical Galton-Watson processes with immigration

In this paper, the asymptotic behavior of the conditional least squares (CLS) estimators of the offspring means $(\alpha ,\beta )$ and of the criticality parameter $\varrho :=\alpha +\beta$ for a $2$-type critical doubly symmetric positively regular Galton-Watson branching process with immigration is described.