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Estimation of the offspring mean in a supercritical branching process with non-stationary immigration

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  • Rahimov, I.

Abstract

In this paper, we consider the conditional least squares estimator (CLSE) of the offspring mean of a branching process with non-stationary immigration based on the observation of population sizes. In the supercritical case, assuming that the immigration variables follow known distributions, conditions guaranteeing the strong consistency of the proposed estimator will be derived. The asymptotic normality of the estimator will also be proved. The proofs are based on direct probabilistic arguments, unlike the previous papers, where functional limit theorems for the process were used.

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  • 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.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:907-914
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    References listed on IDEAS

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    1. Wei, C. Z. & Winnicki, J., 1989. "Some asymptotic results for the branching process with immigration," Stochastic Processes and their Applications, Elsevier, vol. 31(2), pages 261-282, April.
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    Cited by:

    1. 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.

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