ESTIMATORS RELATED TO U-PROCESSES WITH APPLICATIONS TO MULTIVARIATE MEDIANS - ASYMPTOTIC NORMALITY

• 成果类型: Article
• 署名作者: ARCONES, MA; CHEN, ZQ; GINE, E
• 署名单位: William Paterson University New Jersey; University of Connecticut; University of Connecticut
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176325637
• 发表日期: 1994
• 页码: 1460-1477
• 关键词: central limit-theorem; depth

摘要

If a criterion function g(x(1),...,x(m); theta) depends on m > 1 samples, then a natural estimator of arg max P(m)g(x(1),...,x(m); theta) is the arg max of a U-process. It is observed that, under suitable conditions, these estimators are asymptotically normal. This is then applied to prove asymptotic normality of Liu's simplicial median and of Oja's medians in R(d).