CONFIDENCE BANDS IN DENSITY ESTIMATION

• 成果类型: Article
• 署名作者: Gine, Evarist; Nickl, Richard
• 署名单位: University of Connecticut; University of Cambridge
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/09-AOS738
• 发表日期: 2010
• 页码: 1122-1170
• 关键词: Nonparametric regression; gaussian-processes; CONVERGENCE; intervals; rates; sets; approximation; inequalities; adaptation; regions

摘要

Given a sample from some unknown continuous density f : R -> R, we construct adaptive confidence bands that are honest for all densities in a generic subset of the union of t-Holder balls, 0 < t <= r, where r is a fixed but arbitrary integer. The exceptional (nongeneric) set of densities for which our results do not hold is shown to be nowhere dense in the relevant Holder-norm topologies. In the course of the proofs we also obtain limit theorems for maxima of linear wavelet and kernel density estimators, which are of independent interest.