MINIMAXITY OF THE EMPIRICAL DISTRIBUTION FUNCTION IN INVARIANT ESTIMATION

• 成果类型: Article
• 署名作者: YU, QQ; CHOW, MS
• 署名单位: Northeastern University; Sun Yat Sen University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348129
• 发表日期: 1991
• 页码: 935-951
• 关键词: Admissibility

摘要

Consider the problem of continuous invariant estimation of a distribution function with the weighted Cramer-von Mises loss. The minimaxity of the empirical distribution function, which is also the best invariant estimator, is proved for any sample size. This solves a long-standing conjecture.