Minimax estimation of linear functionals over nonconvex parameter spaces

• 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
• 发表日期: 2004
• 页码: 552-576
• 关键词: geometrizing rates; CONVERGENCE

摘要

The minimax theory for estimating linear functionals is extended to the case of a finite union of convex parameter spaces. Upper and lower bounds for the minimax risk can still be described in terms of a modulus of continuity. However in contrast to the theory for convex parameter spaces rate optimal procedures are often required to be nonlinear. A construction of such nonlinear procedures is given. The results developed in this paper have important applications to the theory of adaptation.