Adaptive nonparametric confidence sets

• 成果类型: Article
• 署名作者: Robins, James; Van der Vaart, Aad
• 署名单位: Harvard University; Harvard T.H. Chan School of Public Health; Vrije Universiteit Amsterdam
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000877
• 发表日期: 2006
• 页码: 229-253
• 关键词: gaussian white-noise; DENSITY-ESTIMATION; wavelet shrinkage; anisotropic regression; integral functionals; model selection; random rates; EQUIVALENCE; derivatives; adaptation

摘要

We construct honest confidence regions for a Hilbert space-valued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection of models. The latter adaptation is necessarily limited in scope. We review the notion of adaptive confidence regions, and relate the optimal rates of the diameter of adaptive confidence regions to the minimax rates for testing and estimation. Applications include the finite normal mean model, the white noise model, density estimation and regression with random design.