IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v119y2009i11p3939-3954.html
   My bibliography  Save this article

Bootstrap of the offspring mean in the critical process with a non-stationary immigration

Author

Listed:
  • Rahimov, I.

Abstract

In applications of branching processes, usually it is hard to obtain samples of a large size. Therefore, a bootstrap procedure allowing inference based on a small sample size is very useful. Unfortunately, in the critical branching process with stationary immigration the standard parametric bootstrap is invalid. In this paper, we consider a process with non-stationary immigration, whose mean and variance vary regularly with nonnegative exponents [alpha] and [beta], respectively. We prove that 1+2[alpha] is the threshold for the validity of the bootstrap in this model. If [beta] 1+2[alpha] it is invalid. In the case [beta]=1+2[alpha], the validity of the bootstrap depends on the slowly varying parts of the immigration mean and variance. These results allow us to develop statistical inferences about the parameters of the process in its early stages.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:11:p:3939-3954
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(09)00154-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:119:y:2009:i:11:p:3939-3954. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.