Paul Eggermont
University of Delaware
Title: Equivalent kernels and uniform error bounds for smoothing splines
Almost sure bounds are established for the uniform error of smoothing splines in nonparametric regression with random designs. Some kernel-like properties of the Green's function for an appropriate boundary value problem are needed to reduce the problem to that for kernel-like regression estimators. Then, results of Einmahl and Mason (2005) imply the required bounds, uniformly in the smoothing parameter over a wide range, thus admitting random choices.

The paper(s) may be found at

http://www.udel.edu/FREC/eggermont/Preprints/NiceDesignSplines.pdf
http://www.udel.edu/FREC/eggermont/Preprints/EqKernSpline.pdf
©2006, Department of Mathematical Sciences
Last Modified: March 1, 2006