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February 2011 Immigrated urn models—theoretical properties and applications
Li-Xin Zhang, Feifang Hu, Siu Hung Cheung, Wai Sum Chan
Ann. Statist. 39(1): 643-671 (February 2011). DOI: 10.1214/10-AOS851


Urn models have been widely studied and applied in both scientific and social science disciplines. In clinical studies, the adoption of urn models in treatment allocation schemes has proved to be beneficial to researchers, by providing more efficient clinical trials, and to patients, by increasing the likelihood of receiving the better treatment. In this paper, we propose a new and general class of immigrated urn (IMU) models that incorporates the immigration mechanism into the urn process. Theoretical properties are developed and the advantages of the IMU models are discussed. In general, the IMU models have smaller variabilities than the classical urn models, yielding more powerful statistical inferences in applications. Illustrative examples are presented to demonstrate the wide applicability of the IMU models. The proposed IMU framework, including many popular classical urn models, not only offers a unify perspective for us to comprehend the urn process, but also enables us to generate several novel urn models with desirable properties.


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Li-Xin Zhang. Feifang Hu. Siu Hung Cheung. Wai Sum Chan. "Immigrated urn models—theoretical properties and applications." Ann. Statist. 39 (1) 643 - 671, February 2011.


Published: February 2011
First available in Project Euclid: 15 February 2011

zbMATH: 1226.60012
MathSciNet: MR2797859
Digital Object Identifier: 10.1214/10-AOS851

Primary: 60F15 , 62G10
Secondary: 60F05 , 60F10

Keywords: Adaptive designs , asymptotic normality , birth and death urn , branching process with immigration , clinical trial , drop-the-loser rule , urn model

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 1 • February 2011
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