On M-estimators and normal quantiles

• 成果类型: Article
• 署名作者: Kozek, AS
• 署名单位: Macquarie University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1059655910
• 发表日期: 2003
• 页码: 1170-1185
• 关键词: smoothed empirical processes; WEAK-CONVERGENCE; regression

摘要

This paper explores a class of robust estimators of normal quantiles filling the gap between maximum likelihood estimators and empirical quantiles. Our estimators are linear combinations of M-estimators. Their asymptotic variances can be arbitrarily close to variances of the maximum likelihood estimators. Compared with empirical quantiles, the new estimators offer considerable reduction of variance at near normal probability distributions.