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01月14日浙江大学张立新教授讲座预告
( 来源:   发布日期:2017-01-13 阅读:次)

 

讲座题目Recursive Stochastic Algorithms with Applications to Adaptive Designs

讲 座 人:浙江大学数学科学学院  张立新 教授

讲座时间:20170114日上午9:00

讲座地点:浙江工商大学经济楼328

主讲人简介:

张立新,浙江大学求是特聘教授。1995年获复旦大学理学博士学位, 1997年晋升为教授,2001-2012年担任浙江大学统计学研究所副所长、常务副所长、所长,2009-2015年任浙江大学数学系副主任。现任浙江大学数学科学学院副院长、杭州市钱江特聘专家、IMS-China委员会委员、中国现场统计研究会理事、浙江省现场统计研究会理事长。主要从事概率极限理论、相依数据模型、临床试验自适应随机化设计、随机过程轨道性质等领域的研究,发表了学术论文140多篇,于1998年入选"浙江省跨世纪151人才工程" 2008年入选教育部“新世纪优秀人才支持计划”、2010年获得浙江省自然科学基金杰出青年基金,2012年获得国家自然科学基金杰出青年基金。

Abstract

Stochastic approximation algorithms have been the subject of an enormous body of literature, both theoretical and applied. It is found that a lot of randomization models in clinical trials have strong relationship with the stochastic approximation algorithms. Recently, by using a central limit theorem for the stochastic approximation algorithm, Laruelle and Pages (Ann. Appl. Probab., 2013) derived  the asymptotic normality or central limit theorem for randomized urn models investigated in Bai and Hu (Ann. Appl. Probab., 2005). However, the classical central limit theorem for the stochastic approximation algorithm does not include all cases of its regression function, creating a gap between the results of Laruelle and Pages (2013) and those of Bai and Hu (2005) for randomized urn models. We establish new central limit theorems of the stochastic approximation algorithm under the popular Lindeberg condition to fill this gap. In our applications, we investigate a more involved family of urn models and related adaptive designs in which it is possible to remove the balls from the urn, and the expectation of the total number of  balls updated at each stage is not necessary a constant. The asymptotic properties are derived under much less stringent assumptions than those in Bai and Hu (2005) and Laruelle and Pages (2013). The application of the stochastic approximation approach to other types of adaptive designs will also be discussed. 

欢迎老师和同学们参与讨论。

 

 


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