Probability Seminar
Department of Mathematical Sciences |
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Paul EggermontUniversity 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