The Bahadur-Kiefer representation for U-quantiles

• 成果类型: Article
• 署名作者: Arcones, MA
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1032526976
• 发表日期: 1996
• 页码: 1400-1422
• 关键词: limit-theorems; STOCHASTIC-PROCESSES; iterated logarithm; M-ESTIMATORS; p-variation; statistics; LAW

摘要

We consider the distributional and the almost sure pointwise Bahadur-Kiefer representation for U-quantiles. We show that the order of this representation depends on the order of the local variance of the empirical process of U-statistic structure at the U-quantile. Our results indicate that U-quantiles can be smoother than quantiles. U-quantiles can either be as unsmooth as quantiles or can behave as differentiable statistical functionals.