NONPARAMETRIC REGRESSION, CONFIDENCE REGIONS AND REGULARIZATION

• 成果类型: Article
• 署名作者: Davies, P. L.; Kovac, A.; Meise, M.
• 署名单位: University of Duisburg Essen; University of Bristol; Eindhoven University of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS575
• 发表日期: 2009
• 页码: 2597-2625
• 关键词: multiresolution; maximum; CURVES; tests; balls; bands; sets

摘要

In this paper we offer a unified approach to the problem of nonparametric regression on the unit interval. It is based on a universal, honest and nonasymptotic confidence region A(n) which is defined by a set of linear in-equalities involving the values of the functions at the design points. Interest will typically center on certain simplest functions in A(n) where simplicity can be defined in terms of shape (number of local extremes, intervals of convexity/concavity) or smoothness (bounds on derivatives) or a combination of both. Once some form of regularization has been decided upon the confidence region can be used to provide honest nonasymptotic confidence bounds which are less informative but conceptually much simpler.