Open Access
October 2009 Nonparametric regression, confidence regions and regularization
P. L. Davies, A. Kovac, M. Meise
Ann. Statist. 37(5B): 2597-2625 (October 2009). DOI: 10.1214/07-AOS575


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 $\mathcal{A}_{n}$ which is defined by a set of linear inequalities involving the values of the functions at the design points. Interest will typically center on certain simplest functions in $\mathcal{A}_{n}$ 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.


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P. L. Davies. A. Kovac. M. Meise. "Nonparametric regression, confidence regions and regularization." Ann. Statist. 37 (5B) 2597 - 2625, October 2009.


Published: October 2009
First available in Project Euclid: 17 July 2009

zbMATH: 1173.62023
MathSciNet: MR2541440
Digital Object Identifier: 10.1214/07-AOS575

Primary: 62G08
Secondary: 62G15 , 62G20

Keywords: confidence bands , confidence region , Nonparametric regression , shape regularization , smoothness regularization

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 5B • October 2009
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