UNIFORM BOUNDS FOR NORMS OF SUMS OF INDEPENDENT RANDOM FUNCTIONS

• 成果类型: Article
• 署名作者: Goldenshluger, Alexander; Lepski, Oleg
• 署名单位: University of Haifa; Aix-Marseille Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP595
• 发表日期: 2011
• 页码: 2318-2384
• 关键词: kernel density estimators; Empirical Processes; Concentration inequalities; random-variables; LIMIT-THEOREMS; Consistency; constants; selection; moment

摘要

In this paper, we develop a general machinery for finding explicit uniform probability and moment bounds on sub-additive positive functionals of random processes. Using the developed general technique, we derive uniform bounds on the L-s-norms of empirical and regression-type processes. Usefulness of the obtained results is illustrated by application to the processes appearing in kernel density estimation and in nonparametric estimation of regression functions.