Asymptotics in randomized URN models

• 成果类型: Article
• 署名作者: Bai, ZD; Hu, FF
• 署名单位: Northeast Normal University - China; National University of Singapore; University of Virginia
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051604000000774
• 发表日期: 2005
• 页码: 914-940
• 关键词: multiarm clinical-trials; central limit-theorems; play-winner rule; branching processes; adaptive designs; medical trials; time

摘要

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 nonhomogencity of generating matrices are mild and widely satisfied in applications. Several applications are also discussed.