On local U-statistic processes and the estimation of densities of functions of several sample variables

• 成果类型: Article
• 署名作者: Gine, Evarist; Mason, David M.
• 署名单位: University of Connecticut; University of Delaware
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053607000000154
• 发表日期: 2007
• 页码: 1105-1145
• 关键词: limit-theorems; Empirical Processes; CONVERGENCE; rates; inequalities; Consistency; distances

摘要

A notion of local U-statistic process is introduced and central limit theorems in various norms are obtained for it. This involves the development of several inequalities for U-processes that may be useful in other contexts. This local U-statistic process is based on an estimator of the density of a function of several sample variables proposed by Frees [J. Amer Statist. Assoc. 89 (1994) 517-525] and, as a consequence, uniform in bandwidth central limit theorems in the sup and in the L-p norms are obtained for these estimators.