Confidence balls in Gaussian regression

• 成果类型: Article
• 署名作者: Baraud, Y
• 署名单位: Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000000085
• 发表日期: 2004
• 页码: 528-551
• 关键词: Nonparametric regression; estimators; rates; sets

摘要

Starting from the observation of an R(n)-Gaussian vector of mean f and covariance matrix sigma(2)I(n) (I(n) is the identity matrix), we propose a method for building a Euclidean confidence ball around f, with prescribed probability of coverage. For each n, we describe its nonasymptotic property and show its optimality with respect to some criteria.