Simultaneous sharp estimation of functions and their derivatives

• 成果类型: Article
• 署名作者: Efromovich, S
• 署名单位: University of New Mexico
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 273-278
• 关键词: regression

摘要

A data-driven estimate is given that, over a Sobolev space, is simultaneously asymptotically sharp minimax for estimating both the function and its derivatives under integrated squared error loss. It is also shown that linear estimates cannot be simultaneously asymptotically sharp minimax over a given Sobolev space.