Uniform error bounds for smoothing splines

Details Uniform error bounds for smoothing splines Uniform error bounds for smoothing splines

2006-12-27

arxiv.org/abs/math/0612776v1

IMS Lecture Notes Monograph Series 2006, Vol. 51, 220-237

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/074921706000000879 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/p

Scientific paper

10.1214/074921706000000879

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.

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