The Gaussian approximation for multi-color generalized Friedman’s urn model

作     者：ZHANG LiXin HU FeiFang 

作者机构：Department of MathematicsZhejiang UniversityHangzhou 310027China Department of StatisticsUniversity of VirginiaHalsey HallCharlottesvilleVirginia 22904-4135USA 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2009年第52卷第6期

页      面：1305-1326页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China (Grant No. 10771192) National Science Foundation of USA (Grant No. DMS-0349048) 

主　　题：strong invariance Gaussian approximation the law of iterated logarithm asymptotic normality urn model randomized play-the-winner rule 60F15 62E20 62L05 60F05 62F12 

摘      要：The generalized Friedman’s urn model is a popular urn model which is widely used in many *** particular,it is extensively used in treatment allocation schemes in clinical *** this paper,we show that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a multi-color generalized Friedman’s urn model with both homogeneous and non-homogeneous generating *** Gaussian process is a solution of a stochastic differential *** Gaussian approximation is important for the understanding of the behavior of the urn process and is also useful for statistical *** an application,we obtain the asymptotic properties including the asymptotic normality and the law of the iterated logarithm for a multi-color generalized Friedman s urn model as well as the randomized-play-the-winner rule as a special case.