Institute of Mathematical Statistics Lecture Notes - Monograph Series

Uniform error bounds for smoothing splines

P. P. B. Eggermont and V. N. LaRiccia

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Abstract

Almost sure bounds are established on the uniform error of smoothing spline estimators in nonparametric regression with random designs. Some results of Einmahl and Mason (2005) are used to derive uniform error bounds for the approximation of the spline smoother by an “equivalent” reproducing kernel regression estimator, as well as for proving uniform error bounds on the reproducing kernel regression estimator itself, uniformly in the smoothing parameter over a wide range. This admits data-driven choices of the smoothing parameter.

Chapter information

Source
Evarist Giné, Vladimir Koltchinskii, Wenbo Li, Joel Zinn, eds., High Dimensional Probability: Proceedings of the Fourth International Conference (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 220-237

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196284115

Digital Object Identifier
doi:10.1214/074921706000000879

Mathematical Reviews number (MathSciNet)
MR2387772

Zentralblatt MATH identifier
1117.62039

Subjects
Primary: 62G08: Nonparametric regression 62G20: Asymptotic properties

Keywords
spline smoothing random designs equivalent kernels

Rights
Copyright © 2006, Institute of Mathematical Statistics

Citation

Eggermont, P. P. B.; LaRiccia, V. N. Uniform error bounds for smoothing splines. High Dimensional Probability, 220--237, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000879. https://projecteuclid.org/euclid.lnms/1196284115


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