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Estimation of the variances in the branching process with immigration
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  • Published: March 1991

Estimation of the variances in the branching process with immigration

  • J. Winnicki1 

Probability Theory and Related Fields volume 88, pages 77–106 (1991)Cite this article

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  • 17 Citations

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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.

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Author information

Authors and Affiliations

  1. Department of Statistics, Columbia University, 10027, New York, NY, USA

    J. Winnicki

Authors
  1. J. Winnicki
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Additional information

Research supported by the National Science Foundation under Grant NSF-DMS-8801496

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Cite this article

Winnicki, J. Estimation of the variances in the branching process with immigration. Probab. Th. Rel. Fields 88, 77–106 (1991). https://doi.org/10.1007/BF01193583

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  • Received: 10 July 1989

  • Revised: 02 August 1990

  • Issue Date: March 1991

  • DOI: https://doi.org/10.1007/BF01193583

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Keywords

  • Stochastic Process
  • Probability Theory
  • Full Range
  • Mathematical Biology
  • Analogous Result
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