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A modified bootstrap for branching processes with immigration

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  • Datta, Somnath
  • Sriram, T. N.

Abstract

In this paper we consider bootstrap approximation to the sampling distribution of an estimator of the offspring mean m in a branching process with immigration. A modification of the standard parametric bootstrap procedure is shown to eliminate the invalidity of the standard bootstrap for the case m = 1, as reported in Sriram (1994). Furthermore, the modified bootstrap is shown to provide valid approximations for other values of m ([not equal to] 1) as well. Thus, in this example, the modified bootstrap provides a unified solution while the form of the limit distribution of the estimator of m via classical asymptotic theory depends on m. It is argued that similar modifications will be useful more generally.

Suggested Citation

  • Datta, Somnath & Sriram, T. N., 1995. "A modified bootstrap for branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 275-294, April.
    • Handle: RePEc:eee:spapps:v:56:y:1995:i:2:p:275-294
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    References listed on IDEAS

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    1. Lahiri, Soumendra Nath, 1991. "Second order optimality of stationary bootstrap," Statistics & Probability Letters, Elsevier, vol. 11(4), pages 335-341, April.
    2. Lai, Tze Leung & Wei, Ching Zong, 1983. "Lacunary systems and generalized linear processes," Stochastic Processes and their Applications, Elsevier, vol. 14(2), pages 187-199, February.
    3. 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. M. González & M. Mota & I. Puerto, 2011. "Weighted conditional least square estimators for bisexual branching processes with immigration," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 607-629, November.
    2. Rahimov, I., 2009. "Bootstrap of the offspring mean in the critical process with a non-stationary immigration," Stochastic Processes and their Applications, Elsevier, vol. 119(11), pages 3939-3954, November.
    3. I. Rahimov & M. Omar, 2011. "Validity of the bootstrap in the critical process with a non-stationary immigration," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 1-19.
    4. Miguel González & Inés M. Puerto, 2012. "Diffusion Approximation of an Array of Controlled Branching Processes," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 843-861, September.

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