A Berry-Esseen bound for finite population student's statistic

• 成果类型: Article
• 署名作者: Bloznelis, M
• 署名单位: Vilnius University; Vilnius University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1022677563
• 发表日期: 1999
• 页码: 2089-2108
• 关键词: self-normalized sums; Edgeworth Expansion

摘要

A general and precise Berry-Esseen bound is proved for the Studentized mean based on N random observations drawn without replacement from a finite population. The bound yields the optimal rate O(N-1/2) under minimal conditions. If the Erdos-Renyi condition holds this bound implies the asymptotic normality of Student's statistic and the self-normalized sum.