On sequential estimation for branching processes with immigration

Yongcheng Qi, Jaxk Reeves

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Consider a Galton-Watson process with immigration. The limiting distributions of the non-sequential estimators of the offspring mean have been proved to be drastically different for the critical case and subcritical and supercritical cases. A sequential estimator, proposed by Sriram et al. (Ann. Statist. 19 (1991) 2232), was shown to be asymptotically normal for both the subcritical and critical cases. Based on a certain stopping rule, we construct a class of two-stage estimators for the offspring mean. These estimators are shown to be asymptotically normal for all the three cases. This gives, without assuming any prior knowledge, a unified estimation and inference procedure for the offspring mean.

Original languageEnglish (US)
Pages (from-to)41-51
Number of pages11
JournalStochastic Processes and their Applications
Issue number1-2
StatePublished - 2002


  • Asymptotic normality
  • Branching process
  • Stopping time
  • Two-stage sequential estimator


Dive into the research topics of 'On sequential estimation for branching processes with immigration'. Together they form a unique fingerprint.

Cite this