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VOL. 51 | 2006 Uniform error bounds for smoothing splines
P. P. B. Eggermont, V. N. LaRiccia

Editor(s) Evarist Giné, Vladimir Koltchinskii, Wenbo Li, Joel Zinn

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.

Information

Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1117.62039
MathSciNet: MR2387772

Digital Object Identifier: 10.1214/074921706000000879

Subjects:
Primary: 62G08, 62G20

Rights: Copyright © 2006, Institute of Mathematical Statistics

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