Exact constants for pointwise adaptive estimation under the Riesz transform

• 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
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-004-0348-9
• 发表日期: 2004
• 页码: 441-467
• 关键词: sup-norm; statistical approach; adaptation

摘要

We consider nonparametric estimation of a multivariate function and its partial derivatives at a fixed point when the Riesz transform of the function is observed in Gaussian white noise. We assume that the unknown function belongs to some Sobolev class and construct an estimation procedure which achieves the best asymptotic minimax risk when the smoothness of the function is unknown.