A constrained risk inequality with applications to nonparametric functional estimation

• 成果类型: Article
• 署名作者: Brown, LD; Low, MG
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 2524-2535
• 关键词: Adaptive Estimation; white-noise; RENORMALIZATION; CONVERGENCE; rates

摘要

A general constrained minimum risk inequality is derived. Given two densities f(theta) and f(0) we find a lower bound for the risk at the point theta given an upper bound for the risk at the point 0. The inequality sheds new light on superefficient estimators in the normal location problem and also on an adaptive estimation problem arising in nonparametric functional estimation.