Probability Theory and Related Fields

, Volume 88, Issue 1, pp 77–106 | Cite as

Estimation of the variances in the branching process with immigration

  • J. Winnicki
Article
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Summary

Estimation theory for the variances of the offspring and immigration distributions in a simple branching process with immigration is developed, analogous to the estimation theory for the means given by Wei and Winnicki (1990). Conditional and weighted conditional least squares estimators are considered and their asymptotic properties for the full range of parameters are studied. Nonexistence of consistent estimators in the critical case is established, which complements analogous result of Wei and Winnicki for the supercritical case.

Keywords

Stochastic Process Probability Theory Full Range Mathematical Biology Analogous Result 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • J. Winnicki
    • 1
  1. 1.Department of StatisticsColumbia UniversityNew YorkUSA

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