A new method of normal approximation

• 成果类型: Article
• 署名作者: Chatterjee, Sourav
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/07-AOP370
• 发表日期: 2008
• 页码: 1584-1610
• 关键词: CENTRAL-LIMIT-THEOREM; steins method; asymptotic-distribution; multivariate clt

摘要

We introduce a new version of Stein's method that reduces a large class of normal approximation problems to variance bounding exercises, thus making a connection between central limit theorems and concentration of measure. Unlike Skorokhod embeddings, the object whose variance Must be bounded has an explicit formula that makes it possible to carry out the program more easily. As an application, we derive a general CLT for functions that are obtained as combinations of many local contributions, where the definition of local itself depends on the data. Several examples are given, including the solution to a nearest-neighbor CLT problem posed by P. Bickel.