Confidence sets for nonparametric wavelet regression

• 成果类型: Article
• 署名作者: Genovese, CR; Wasserman, L
• 署名单位: Carnegie Mellon University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000011
• 发表日期: 2005
• 页码: 698-729
• 关键词: curve estimation; shrinkage; estimators; intervals

摘要

We construct nonparametric confidence sets for regression functions using wavelets that are uniform over Besov balls. We consider both thresholding and modulation estimators for the wavelet coefficients. The confidence set is obtained by showing that a pivot process, constructed from the loss function, converges uniformly to a mean zero Gaussian process. Inverting this pivot yields a confidence set for the wavelet coefficients, and from this we obtain confidence sets on functionals of the regression curve.