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Fixed precision estimator of the offspring mean in branching processes

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  • Shete, Sanjay
  • Sriram, T. N.

Abstract

For the problem of estimating the offspring mean of a branching process with immigration, we propose a modification of the sequential estimator of considered in Sriram et al. (, Ann. Statist.) and study its nonasymptotic and asymptotic properties. In the nonasymptotic setting, it is shown that the modified estimator is unbiased and has bounded mean squared error (MSE) for all , while the estimator in Sriram et al. is biased and a theoretical bound for its MSE is difficult to obtain. The above result is established for the cases of known and unknown offspring variances, separately. In the asymptotic setting, for the case of , it is shown that the modified sequential estimator is as efficient as the sequential estimator in Sriram et al. The theoretical results are supported through simulations. Finally, asymptotic normality of the stopping time, for the case of known offspring variance, is also established.

Suggested Citation

  • Shete, Sanjay & Sriram, T. N., 1998. "Fixed precision estimator of the offspring mean in branching processes," Stochastic Processes and their Applications, Elsevier, vol. 77(1), pages 17-33, September.
    • Handle: RePEc:eee:spapps:v:77:y:1998:i:1:p:17-33
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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. 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. Qi, Yongcheng & Reeves, Jaxk, 0. "On sequential estimation for branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 100(1-2), pages 41-51, July.
    2. Kohtaro Hitomi & Keiji Nagai & Yoshihiko Nishiyama & Junfan Tao, 2021. "Joint Asymptotic Properties of Stopping Times and Sequential Estimators for Stationary First-order Autoregressive Models," KIER Working Papers 1060, Kyoto University, Institute of Economic Research.

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