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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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

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

First available in Project Euclid: 28 November 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

spline smoothing random designs equivalent kernels

Copyright © 2006, Institute of Mathematical Statistics


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.

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