Optimal adaptive estimation of a quadratic functional

• 成果类型: Article
• 署名作者: Cai, T. Tony; Low, Mark G.
• 署名单位: University of Pennsylvania
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000849
• 发表日期: 2006
• 页码: 2298-2325
• 关键词: model selection; linear functionals; sharp; CONVERGENCE; rates

摘要

Adaptive estimation of a quadratic functional over both Besov and L(p) balls is considered. A collection of nonquadratic estimators are developed which have useful bias and variance properties over individual Besov and L(p) balls. An adaptive procedure is then constructed based on penalized maximization over this collection of nonquadratic estimators. This procedure is shown to be optimally rate adaptive over the entire range of Besov and L(p) balls in the sense that it attains certain constrained risk bounds.