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Title: Asymptotics in randomized urn models
Authors: Bai, Z.-D. 
Hu, F.
Keywords: Asymptotic normality
Extended pólya's urn models
Generalized friedman's urn model
Nonhomogeneous generating matrix
Response-adaptive designs
Strong consistency
Issue Date: Feb-2005
Citation: Bai, Z.-D., Hu, F. (2005-02). Asymptotics in randomized urn models. Annals of Applied Probability 15 (1 B) : 914-940. ScholarBank@NUS Repository.
Abstract: This paper studies a very general urn model stimulated by designs in clinical trials, where the number of balls of different types added to the urn at trial n depends on a random outcome directed by the composition at trials 1, 2, . . ., n - 1. Patient treatments are allocated according to types of balls. We establish the strong consistency and asymptotic normality for both the urn composition and the patient allocation under general assumptions on random generating matrices which determine how balls are added to the urn. Also we obtain explicit forms of the asymptotic variance-covariance matrices of both the urn composition and the patient allocation. The conditions on the nonhomogeneity of generating matrices are mild and widely satisfied in applications. Several applications are also discussed. © Institute of Mathematical Statistics, 2005.
Source Title: Annals of Applied Probability
ISSN: 10505164
DOI: 10.1214/105051604000000774
Appears in Collections:Staff Publications

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