ASYMPTOTIC EQUIVALENCE OF FUNCTIONAL LINEAR REGRESSION AND A WHITE NOISE INVERSE PROBLEM

• 成果类型: Article
• 署名作者: Meister, Alexander
• 署名单位: University of Rostock
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS872
• 发表日期: 2011
• 页码: 1471-1495
• 关键词: Nonparametric regression; estimators; prediction

摘要

We consider the statistical experiment of functional linear regression (FLR). Furthermore, we introduce a white noise model where one observes an Ito process, which contains the covariance operator of the corresponding FLR model in its construction. We prove asymptotic equivalence of FLR and this white noise model in LeCam's sense under known design distribution. Moreover, we show equivalence of FLR and an empirical version of the white noise model for finite sample sizes. As an application, we derive sharp minimax constants in the FLR model which are still valid in the case of unknown design distribution.