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Estimation of the mean in partially observed branching processes with general immigration

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  • I. Rahimov

    (Zayed University)

Abstract

In the paper we investigate asymptotic properties of the branching process with non-stationary immigration which are sufficient for a natural estimator of the offspring mean based on partial observations to be strongly consistent and asymptotically normal. The estimator uses only a binomially distributed subset of the population of each generation. This approach allows us to obtain results without conditions on the criticality of the process which makes possible to develop a unified estimation procedure without knowledge of the range of the offspring mean. These results are to be contrasted with the existing literature related to i.i.d. immigration case where the asymptotic normality depends on the criticality of the process and are new for the fully observed processes as well. Examples of applications in the process with immigration with regularly varying mean and variance and subcritical processes with i.i.d. immigration are also considered.

Suggested Citation

  • I. Rahimov, 2019. "Estimation of the mean in partially observed branching processes with general immigration," Statistical Inference for Stochastic Processes, Springer, vol. 22(1), pages 143-155, April.
    • Handle: RePEc:spr:sistpr:v:22:y:2019:i:1:d:10.1007_s11203-017-9170-8
    DOI: 10.1007/s11203-017-9170-8
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    References listed on IDEAS

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    1. Sriram, T. N., 1991. "On the uniform strong consistency of an estimator of the offspring mean in a branching process with immigration," Statistics & Probability Letters, Elsevier, vol. 12(2), pages 151-155, August.
    2. Ronald Meester & Jan Koning & Mart C. M. Jong & Odo Diekmann, 2002. "Modeling and Real-Time Prediction of Classical Swine Fever Epidemics," Biometrics, The International Biometric Society, vol. 58(1), pages 178-184, March.
    3. I. Rahimov, 2016. "Estimation of the offspring mean in a branching process with non stationary immigration," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(19), pages 5619-5627, October.
    4. Rahimov, I., 2011. "Estimation of the offspring mean in a supercritical branching process with non-stationary immigration," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 907-914, August.
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