Asymptotic equivalence for nonparametric regression with multivariate and random design

• 成果类型: Article
• 署名作者: Reiss, Markus
• 署名单位: Ruprecht Karls University Heidelberg
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS525
• 发表日期: 2008
• 页码: 1957-1982
• 关键词: gaussian white-noise; DENSITY-ESTIMATION

摘要

We show that nonparametric regression is asymptotically equivalent, in Le Cam's sense, to a sequence of Gaussian white noise experiments as the number of observations tends to infinity. We propose a general constructive framework, based on approximation spaces, which allows asymptotic equivalence to be achieved, even in the cases of multivariate and random design.