FUNCTIONAL LAWS OF THE ITERATED LOGARITHM FOR LOCAL EMPIRICAL PROCESSES INDEXED BY SETS

• 成果类型: Article
• 署名作者: DEHEUVELS, P; MASON, DM
• 署名单位: University of Delaware
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988617
• 发表日期: 1994
• 页码: 1619-1661
• 关键词: central limit-theorem; quantile processes

摘要

We introduce the notion of a multivariate local (and tail) empirical process indexed by sets and establish a number of functional laws of the iterated logarithm for such processes. This leads to a unified methodology to study the almost sure behavior of various statistics which are local functionals of the empirical distribution. Such statistics include density estimators and the Bahadur-Kiefer representation.