A uniform functional law of the logarithm for the local empirical process

• 成果类型: Article
• 署名作者: Mason, DM
• 署名单位: University of Delaware
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000243
• 发表日期: 2004
• 页码: 1391-1418
• 关键词: iterated logarithm; oscillation behavior; Consistency; rates; approximation; estimators; THEOREM

摘要

We prove a uniform functional law of the logarithm for the local empirical process. To accomplish this we combine techniques from classical and abstract empirical process theory, Gaussian distributional approximation and probability on Banach spaces. The body of techniques we develop should prove useful to the study of the strong consistency of d-variate kernel-type nonparametric function estimators.