On adaptive estimation of linear functionals

• 成果类型: Article
• 署名作者: Cai, TT; Low, MG
• 署名单位: University of Pennsylvania
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000633
• 发表日期: 2005
• 页码: 2311-2343
• 关键词: gaussian white-noise; DENSITY-ESTIMATION; asymptotic equivalence; RECOVERY

摘要

Adaptive estimation of linear functionals over a collection of parameter spaces is considered. A between-class modulus of continuity, a geometric quantity, is shown to be instrumental in characterizing the degree of adaptability over two parameter spaces in the same way that the usual modulus Of Continuity captures the minimax difficulty of estimation over a single parameter space. A general construction of optimally adaptive estimators based on an ordered modulus of continuity is given. The results are complemented by several illustrative examples.