BOUNDS ON THE CONSTANT IN THE MEAN CENTRAL LIMIT THEOREM

• 成果类型: Article
• 署名作者: Goldstein, Larry
• 署名单位: University of Southern California
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP527
• 发表日期: 2010
• 页码: 1672-1689
• 关键词: zero

摘要

Let X-1, X-n be independent with zero means, finite variances sigma(2)(1), sigma(2)(n) and finite absolute third moments Let F-n be the distribution function of (X-1 + + X-n)/sigma where sigma(2) = Sigma(n)(t=1) sigma(2)(t), and Phi that of the standard normal The L-1-distance between F-n and Phi then satisfies parallel to F-n-Phi parallel to(1) <= 1/sigma(3) (n)Sigma E-t=1 vertical bar X-t vertical bar(3) In particular, when X-1. X-n are identically distributed with variance sigma(2). we have parallel to F-n-Phi parallel to 1 <= E vertical bar X-1 vertical bar(3)/sigma(3)root n for all n is an element of N. corresponding to an L-1-Berry-Esseen constant of 1