Uniform error bounds for smoothing splines

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dc.creatorEggermont, P. P. B.
dc.creatorLaRiccia, V. N.
dc.date2006-12-27
dc.date.accessioned2026-07-07T08:08:30Z
dc.date.available2026-07-07T08:08:30Z
dc.descriptionAlmost 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.
dc.descriptionPublished at http://dx.doi.org/10.1214/074921706000000879 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0612776
dc.identifierhttp://arxiv.org/abs/math/0612776
dc.identifierIMS Lecture Notes Monograph Series 2006, Vol. 51, 220-237
dc.identifierdoi:10.1214/074921706000000879
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131286
dc.subjectStatistics Theory
dc.subject62G08, 62G20 (Primary)
dc.titleUniform error bounds for smoothing splines
dc.typetext

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