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November 2002 Gaussian approximation theorems for urn models and their applications
Z. D. Bai, Feifang Hu, Li-Xin Zhang
Ann. Appl. Probab. 12(4): 1149-1173 (November 2002). DOI: 10.1214/aoap/1037125857


We consider weak and strong Gaussian approximations for a two-color generalized Friedman's urn model with homogeneous and nonhomogeneous generating matrices. In particular, the functional central limit theorems and the laws of iterated logarithm are obtained. As an application, we obtain the asymptotic properties for the randomized-play-the-winner rule. Based on the Gaussian approximations, we also get some variance estimators for the urn model.


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Z. D. Bai. Feifang Hu. Li-Xin Zhang. "Gaussian approximation theorems for urn models and their applications." Ann. Appl. Probab. 12 (4) 1149 - 1173, November 2002.


Published: November 2002
First available in Project Euclid: 12 November 2002

zbMATH: 1014.60025
MathSciNet: MR1936587
Digital Object Identifier: 10.1214/aoap/1037125857

Primary: 62G10
Secondary: 60F15 , 62E10

Keywords: functional central limit theorems , Gaussian approximation , nonhomogeneous generating matrix , randomized play-the-winner rule , the law of iterated logarithm , urn model

Rights: Copyright © 2002 Institute of Mathematical Statistics


Vol.12 • No. 4 • November 2002
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