Sharp adaptive estimation of linear functionals

• 成果类型: Article
• 署名作者: Klemelä, J; Tsybakov, AB
• 署名单位: Ruprecht Karls University Heidelberg; Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2001
• 页码: 1567-1600
• 关键词: sup-norm; asymptotic equivalence; DENSITY-ESTIMATION; pointwise; rates; RISK; adaptation; selection

摘要

We consider estimation of a linear functional T(f) where f is an unknown function observed in Gaussian white noise. We find asymptotically sharp adaptive estimators on various scales of smoothness classes in multidimensional situations, The results allow evaluating explicitly the effect of dimension and treating general scales of classes. Furthermore, we establish a connection between sharp adaptation and optimal recovery. Namely, we propose a scheme that reduces the construction of sharp adaptive estimators on a scale of functional classes to a solution of the corresponding optimization problem.