IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v24y2022i1d10.1007_s11009-021-09858-6.html
   My bibliography  Save this article

Nonlinear Unbalanced Urn Models via Stochastic Approximation

Author

Listed:
  • Soumaya Idriss

    (University of Monastir)

Abstract

This paper presents a link between unbalanced non-linear urn model (a two-colored urn model) and stochastic approximation theory. Findings of our study reveal a successful establishment of limit laws for the urn composition, obtained under a drawing rule reinforced by an ℝ + $\mathbb {R}_{+}$ -valued concave function and a non-balanced replacement matrix.

Suggested Citation

  • Soumaya Idriss, 2022. "Nonlinear Unbalanced Urn Models via Stochastic Approximation," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 413-430, March.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:1:d:10.1007_s11009-021-09858-6
    DOI: 10.1007/s11009-021-09858-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-021-09858-6
    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/s11009-021-09858-6?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. Bai, Z. D. & Hu, Feifang & Shen, Liang, 2002. "An Adaptive Design for Multi-Arm Clinical Trials," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 1-18, April.
    2. Bai, Z. D. & Hu, Feifang, 1999. "Asymptotic theorems for urn models with nonhomogeneous generating matrices," Stochastic Processes and their Applications, Elsevier, vol. 80(1), pages 87-101, March.
    Full references (including those not matched with items on IDEAS)

    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. Li-Xin, Zhang, 2006. "Asymptotic results on a class of adaptive multi-treatment designs," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 586-605, March.
    2. Davidson, Allison & D. Ward, Mark, 2018. "The characterization of tenable Pólya urns," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 38-43.
    3. Aletti, Giacomo & Ghiglietti, Andrea, 2017. "Interacting generalized Friedman’s urn systems," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2650-2678.
    4. Yanqing Yi & Yuan Yuan, 2013. "An optimal allocation for response-adaptive designs," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(9), pages 1996-2008, September.
    5. Yang, Li & Hu, Jiang & Bai, Zhidong, 2024. "Revisit of a Diaconis urn model," Stochastic Processes and their Applications, Elsevier, vol. 172(C).
    6. Yuan, Ao & Chai, Gen Xiang, 2008. "Optimal adaptive generalized Polya urn design for multi-arm clinical trials," Journal of Multivariate Analysis, Elsevier, vol. 99(1), pages 1-24, January.
    7. Moler, José A. & Plo, Fernando & San Miguel, Miguel, 2006. "An adaptive design for clinical trials with non-dichotomous response and prognostic factors," Statistics & Probability Letters, Elsevier, vol. 76(17), pages 1940-1946, November.
    8. Bélisle, Claude & Melfi, Vince, 2008. "Independence after adaptive allocation," Statistics & Probability Letters, Elsevier, vol. 78(3), pages 214-224, February.
    9. Janson, Svante, 2004. "Functional limit theorems for multitype branching processes and generalized Pólya urns," Stochastic Processes and their Applications, Elsevier, vol. 110(2), pages 177-245, April.
    10. Bai, Z. D. & Hu, Feifang & Shen, Liang, 2002. "An Adaptive Design for Multi-Arm Clinical Trials," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 1-18, April.

    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:metcap:v:24:y:2022:i:1:d:10.1007_s11009-021-09858-6. 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.