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March, 1993 A New Class of Kernels for Nonparametric Curve Estimation
Karen Messer, Larry Goldstein
Ann. Statist. 21(1): 179-195 (March, 1993). DOI: 10.1214/aos/1176349021

Abstract

We introduce a new class of variable kernels which depend on the smoothing parameter b through a simple scaling operation, and which have good integrated mean square error (IMSE) convergence properties. These kernels deform "automatically" near the boundary, eliminating boundary bias. Computational formulas are given for all orders of kernel in terms of exponentially damped sines and cosines. The kernel is a computationally convenient approximation to a certain Green's function, with the resulting kernel estimate closely related to a smoothing spline estimate.

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Karen Messer. Larry Goldstein. "A New Class of Kernels for Nonparametric Curve Estimation." Ann. Statist. 21 (1) 179 - 195, March, 1993. https://doi.org/10.1214/aos/1176349021

Information

Published: March, 1993
First available in Project Euclid: 12 April 2007

zbMATH: 0777.62041
MathSciNet: MR1212172
Digital Object Identifier: 10.1214/aos/1176349021

Subjects:
Primary: 62G07
Secondary: 62J02

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.21 • No. 1 • March, 1993
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