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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
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    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.
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    Cited by:

    1. 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.
    2. 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.
    3. Riccardo Gatto, 2019. "Saddlepoint Approximation for Data in Simplices: A Review with New Applications," Stats, MDPI, vol. 2(1), pages 1-27, February.

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