ON THE BERRY-ESSEEN BOUND FOR L-STATISTICS IN THE NON-ID CASE WITH APPLICATIONS TO THE ESTIMATION OF LOCATION PARAMETERS

• 成果类型: Article
• 署名作者: XIANG, XJ
• 署名单位: University of Chicago
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325506
• 发表日期: 1994
• 页码: 968-979
• 关键词: U-STATISTICS; THEOREM

摘要

In this paper, two versions of the Berry-Esseen theorems are established for L-statistics in the non-identically distributed case. One theorem, which requires E\X(i)\(3) < infinity, is an extension of the classical Berry-Esseen theorem. Another, proved under the condition E\X(i)\(alpha) < infinity for some alpha is an element of (0, 1], seems to be of more interest for statistical inference. Some applications are also discussed.