A Note on Estimation of Parameters for Branching Processes with Immigration

Abstract

It is proved that under certain conditions the conditional least-squares estimator of the offspring mean for a sequence of nearly critical Jiřina processes with immigration is consistent but not asymptotically normal and the conditional least-squares estimator of the immigration mean is not consistent. These results differ from the existing results in the case where the initial values are zero (see Ispány et al., 2005).

Keywords:

• Asymptotic behavior
• Branching process with immigration
• Conditional least-squares estimator

Mathematics Subject Classification:

• 60F12
• 60J80