IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v82y1999i1p89-125.html
   My bibliography  Save this article

Compound Poisson approximation in total variation

Author

Listed:
  • Barbour, A. D.
  • Utev, Sergey

Abstract

Poisson approximation in total variation can be successfully established in a wide variety of contexts, involving sums of weakly dependent random variables which usually take the value 0, and occasionally the value 1. If the random variables can take other positive integer values, or if there is stronger dependence between them, compound Poisson approximation may be more suitable. Stein's method, which is so effective in the Poisson context, turns out to be much more difficult to apply for compound Poisson approximation, because the solutions of the Stein equation have undesirable properties. In this paper, we prove new bounds on the absolute values of the solutions to the Stein equation and of their first differences, over certain ranges of their arguments. These enable compound Poisson approximation in total variation to be carried out with almost the same efficiency as in the Poisson case. Even for sums of independent random variables, which have been exhaustively studied in the past, new results are obtained, effectively solving a problem discussed by Le Cam (1965, Bernoulli, Bayes, Laplace. Springer, New York, pp. 179-202), in the context of nonnegative integer valued random variables.

Suggested Citation

  • Barbour, A. D. & Utev, Sergey, 1999. "Compound Poisson approximation in total variation," Stochastic Processes and their Applications, Elsevier, vol. 82(1), pages 89-125, July.
    • Handle: RePEc:eee:spapps:v:82:y:1999:i:1:p:89-125
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(99)00004-6
    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.

    Citations

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


    Cited by:

    1. Pierre Perron & Zhongjun Qu, 2007. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts," Boston University - Department of Economics - Working Papers Series wp2007-044, Boston University - Department of Economics.
    2. Bertanha, Marinho & Moreira, Marcelo J., 2020. "Impossible inference in econometrics: Theory and applications," Journal of Econometrics, Elsevier, vol. 218(2), pages 247-270.
    3. Hashorva, Enkelejd & Hüsler, Jürg, 2002. "Remarks on compound Poisson approximation of Gaussian random sequences," Statistics & Probability Letters, Elsevier, vol. 57(1), pages 1-8, March.
    4. Cong, Tianshu & Xia, Aihua & Zhang, Fuxi, 2020. "A large sample property in approximating the superposition of i.i.d. finite point processes," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4493-4511.
    5. Gan, H.L. & Xia, A., 2015. "Stein’s method for conditional compound Poisson approximation," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 19-26.

    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:82:y:1999:i:1:p:89-125. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.