IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v135y2018icp38-43.html
   My bibliography  Save this article

The characterization of tenable Pólya urns

Author

Listed:
  • Davidson, Allison
  • D. Ward, Mark

Abstract

We characterize tenable Pólya urn schemes via a decomposition of their replacement matrices into small submatrices with certain conditions on the determinants. The characterization also involves an interplay between the submatrices and the initial conditions, as well as certain divisibility conditions.

Suggested Citation

  • Davidson, Allison & D. Ward, Mark, 2018. "The characterization of tenable Pólya urns," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 38-43.
    • Handle: RePEc:eee:stapro:v:135:y:2018:i:c:p:38-43
    DOI: 10.1016/j.spl.2017.11.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016771521730367X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2017.11.013?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, 1999. "Asymptotic theorems for urn models with nonhomogeneous generating matrices," Stochastic Processes and their Applications, Elsevier, vol. 80(1), pages 87-101, March.
    2. Gouet, Raúl, 1989. "A martingale approach to strong convergence in a generalized Pólya-Eggenberger urn model," Statistics & Probability Letters, Elsevier, vol. 8(3), pages 225-228, August.
    3. Hajime Yamato, 1993. "A pólya urn model with a continuum of colors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 453-458, September.
    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. Soumaya Idriss, 2022. "Nonlinear Unbalanced Urn Models via Stochastic Approximation," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 413-430, March.
    2. Charalambos A. Charalambides, 2007. "Distributions of Random Partitions and Their Applications," Methodology and Computing in Applied Probability, Springer, vol. 9(2), pages 163-193, June.
    3. Matthews, Peter C. & Rosenberger, William F., 1997. "Variance in randomized play-the-winner clinical trials," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 233-240, October.
    4. 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.
    5. 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.
    6. Aletti, Giacomo & Ghiglietti, Andrea, 2017. "Interacting generalized Friedman’s urn systems," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2650-2678.
    7. Sibuya, Masaaki & Yamato, Hajime, 1995. "Ordered and unordered random partitions of an integer and the GEM distribution," Statistics & Probability Letters, Elsevier, vol. 25(2), pages 177-183, November.
    8. 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.
    9. 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.
    10. Gopal K. Basak & Amites Dasgupta, 2006. "Central and Functional Central Limit Theorems for a Class of Urn Models," Journal of Theoretical Probability, Springer, vol. 19(3), pages 741-756, December.
    11. 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.
    12. Kotz, Samuel & Mahmoud, Hosam & Robert, Philippe, 2000. "On generalized Pólya urn models," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 163-173, August.

    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:stapro:v:135:y:2018:i:c:p:38-43. 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/622892/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.