On estimation of the variances for critical branching processes with immigration

Chunhua Ma, Longmin Wang
2010 Journal of Applied Probability  
The conditional least-squares estimators of the variances are studied for a critical branching process with immigration that allows the offspring distributions to have infinite fourth moments. We derive different forms of limiting distributions for these estimators when the offspring distributions have regularly varying tails with index α. In particular, in the case in which 2 < α < 8/3, the normalizing factor of the estimator for the offspring variance is smaller than √n, which is different from that of Winnicki (1991).
doi:10.1239/jap/1276784907 fatcat:sjfl2bljhbftfe4mdtvojmejke