Minimax linear estimation in a white noise problem

• 成果类型: Article
• 署名作者: Zhao, LH
• 署名单位: University of Pennsylvania
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 745-755
• 关键词: asymptotic equivalence; DENSITY-ESTIMATION; optimal recovery; RENORMALIZATION; CONVERGENCE; rates; RISK

摘要

Linear estimation of f(x) at a point in a white noise model is considered. The exact linear minimax estimator of f(0) is found for the family of f(x) in which f'(x) is Lip(M). The resulting estimator is then used to verify a conjecture of Sacks and Ylvisaker concerning the near optimality of the Epanechnikov kernel.