STRONG MODERATE DEVIATION THEOREMS

• 成果类型: Article
• 署名作者: INGLOT, T; KALLENBERG, WCM; LEDWINA, T
• 署名单位: University of Twente
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989814
• 发表日期: 1992
• 页码: 987-1003
• 关键词: linear rank statistics; local limit-theorems; gauss space

摘要

Strong moderate deviation theorems are concerned with relative errors in the tails caused by replacing the exact distribution function by its limiting distribution function. A new approach for deriving such theorems is presented using strong approximation inequalities. In this way a strong moderate deviation theorem is obtained for statistics of the form T(alpha(n)), where T is a sublinear functional and alpha(n) is the empirical process. The basic theorem is also applied on linear combinations of order statistics, leading to a substantial improvement of previous results.