Gaussian approximation theorems for urn models and their applications

• 成果类型: Article
• 署名作者: Bai, ZD; Hu, FF; Zhang, LX
• 署名单位: National University of Singapore; University of Virginia; Zhejiang University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2002
• 页码: 1149-1173
• 关键词: CENTRAL LIMIT-THEOREMS; adaptive designs; medical trials

摘要

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.