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Central limit theorems for urn models

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  • Smythe, R. T.

Abstract

We consider central limit theory for urn models in which balls are not necessarily replaced after being drawn, giving rise to negative diagonal entries in the generating matrix. Under conditions on the eigenvalues and eigenvectors, we give results both for the contents of the urn and the number of times balls of each type are drawn.

Suggested Citation

  • Smythe, R. T., 1996. "Central limit theorems for urn models," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 115-137, December.
    • Handle: RePEc:eee:spapps:v:65:y:1996:i:1:p:115-137
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    Citations

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    Cited by:

    1. 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.
    2. Yi, Yanqing & Wang, Xikui, 2007. "Goodness-of-fit test for response adaptive clinical trials," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 1014-1020, June.
    3. Yang, Li & Hu, Jiang & Bai, Zhidong, 2024. "Revisit of a Diaconis urn model," Stochastic Processes and their Applications, Elsevier, vol. 172(C).
    4. Aletti, Giacomo & Ghiglietti, Andrea, 2017. "Interacting generalized Friedman’s urn systems," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2650-2678.
    5. 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.
    6. 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.
    7. Soumaya Idriss & Hosam Mahmoud, 2023. "Exact Covariances and Refined Asymptotics in Dichromatic Tenable Balanced Pólya Urn Schemes," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-16, June.
    8. Kotz, Samuel & Mahmoud, Hosam & Robert, Philippe, 2000. "On generalized Pólya urn models," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 163-173, August.
    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.
    11. Feng, Yarong & Mahmoud, Hosam M., 2021. "Dynamic Pólya–Eggenberger urns," Statistics & Probability Letters, Elsevier, vol. 174(C).
    12. 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.
    13. Dasgupta, Amites, 2024. "Azuma-Hoeffding bounds for a class of urn models," Statistics & Probability Letters, Elsevier, vol. 204(C).

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