SPATIALLY-ADAPTIVE SENSING IN NONPARAMETRIC REGRESSION

• 成果类型: Article
• 署名作者: Bull, Adam D.
• 署名单位: University of Cambridge
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS1064
• 发表日期: 2013
• 页码: 41-62
• 关键词: variable bandwidth; confidence bands; DESIGN; adaptation

摘要

While adaptive sensing has provided improved rates of convergence in sparse regression and classification, results in nonparametric regression have so far been restricted to quite specific classes of functions. In this, paper, we describe an adaptive-sensing algorithm which is applicable to general nonparametric-regression problems. The algorithm is spatially adaptive, and achieves improved rates of convergence over spatially inhomogeneous functions. Over standard function classes, it likewise retains the spatial adaptivity properties of a uniform design.