IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v27y2014i3d10.1007_s10959-012-0454-z.html
   My bibliography  Save this article

On Edgeworth Expansions in Generalized Urn Models

Author

Listed:
  • S. M. Mirakhmedov

    (Institute of Mathematics and Information Technologies)

  • S. Rao Jammalamadaka

    (University of California)

  • Ibrahim B. Mohamed

    (University of Malaya)

Abstract

The random vector of frequencies in a generalized urn model can be viewed as conditionally independent random variables, given their sum. Such a representation is exploited here to derive Edgeworth expansions for a “sum of functions of such frequencies,” which are also called “decomposable statistics.” Applying these results to urn models such as with- and without-replacement sampling schemes as well as the multicolor Pólya–Egenberger model, new results are obtained for the chi-square statistic, for the sample sum in a without-replacement scheme, and for the so-called Dixon statistic that is useful in comparing two samples.

Suggested Citation

  • S. M. Mirakhmedov & S. Rao Jammalamadaka & Ibrahim B. Mohamed, 2014. "On Edgeworth Expansions in Generalized Urn Models," Journal of Theoretical Probability, Springer, vol. 27(3), pages 725-753, September.
  • Handle: RePEc:spr:jotpro:v:27:y:2014:i:3:d:10.1007_s10959-012-0454-z
    DOI: 10.1007/s10959-012-0454-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-012-0454-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10959-012-0454-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Babu, G. Jogesh & Singh, Kesar, 1985. "Edgeworth expansions for sampling without replacement from finite populations," Journal of Multivariate Analysis, Elsevier, vol. 17(3), pages 261-278, December.
    2. Mirakhmedov, Sherzod A., 2005. "Lower estimation of the remainder term in the CLT for a sum of the functions of k-spacings," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 411-424, July.
    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. Dolgopyat, Dmitry & Hafouta, Yeor, 2022. "Edgeworth expansions for independent bounded integer valued random variables," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 486-532.
    2. Riccardo Gatto, 2019. "Saddlepoint Approximation for Data in Simplices: A Review with New Applications," Stats, MDPI, vol. 2(1), pages 1-27, February.
    3. Jessica Gronsbell & Molei Liu & Lu Tian & Tianxi Cai, 2022. "Efficient evaluation of prediction rules in semi‐supervised settings under stratified sampling," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1353-1391, 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. Ibrahim Bin Mohamed & Sherzod M. Mirakhmedov, 2016. "Approximation by Normal Distribution for a Sample Sum in Sampling Without Replacement from a Finite Population," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 188-220, August.
    2. Sherzod Mirakhmedov & Syed Tirmizi & Muhammad Naeem, 2011. "A Cramér-type large deviation theorem for sums of functions of higher order non-overlapping spacings," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(1), pages 33-54, July.
    3. Gutti Babu & Kesar Singh & Yaning Yang, 2003. "Edgeworth expansions for compound Poisson processes and the bootstrap," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(1), pages 83-94, March.
    4. Zhonglei Wang & Liuhua Peng & Jae Kwang Kim, 2022. "Bootstrap inference for the finite population mean under complex sampling designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1150-1174, September.
    5. Gutti Babu, 1992. "Subsample and half-sample methods," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(4), pages 703-720, December.
    6. Politis, Dimitris N. & Wolf, Michael & Romano, Joseph P., 1999. "Subsampling, symmetrization, and robust interpolation," DES - Working Papers. Statistics and Econometrics. WS 6343, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Fang Han, 2024. "An Introduction to Permutation Processes (version 0.5)," Papers 2407.09664, arXiv.org.
    8. Rahul Singh & Neeraj Misra, 2023. "Some parametric tests based on sample spacings," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 211-231, March.
    9. M. Ekström & S. M. Mirakhmedov & S. Rao Jammalamadaka, 2020. "A class of asymptotically efficient estimators based on sample spacings," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 617-636, September.

    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:spr:jotpro:v:27:y:2014:i:3:d:10.1007_s10959-012-0454-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.