The Annals of Statistics

Immigrated urn models—theoretical properties and applications

Li-Xin Zhang, Feifang Hu, Siu Hung Cheung, and Wai Sum Chan

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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.

Article information

Ann. Statist., Volume 39, Number 1 (2011), 643-671.

First available in Project Euclid: 15 February 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F15: Strong theorems 62G10: Hypothesis testing
Secondary: 60F05: Central limit and other weak theorems 60F10: Large deviations

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


Zhang, Li-Xin; Hu, Feifang; Cheung, Siu Hung; Chan, Wai Sum. Immigrated urn models—theoretical properties and applications. Ann. Statist. 39 (2011), no. 1, 643--671. doi:10.1214/10-AOS851.

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