Adaptive confidence bands

• 成果类型: Article
• 署名作者: Genovese, Christopher; Wasserman, Larry
• 署名单位: Carnegie Mellon University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS500
• 发表日期: 2008
• 页码: 875-905
• 关键词: Nonparametric regression; DENSITY-ESTIMATION; intervals; rates; sets; inference; selection; balls

摘要

We show that there do not exist adaptive confidence bands for curve estimation except under very restrictive assumptions. We propose instead to construct adaptive bands that cover a surrogate function f* which is close to, but simpler than, f. The surrogate captures the significant features in f. We establish lower bounds on the width for any confidence band for f* and construct a procedure that comes within a small constant factor of attaining the lower bound for finite-samples.