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June, 1991 A Comparison of a Spline Estimate to its Equivalent Kernel Estimate
K. Messer
Ann. Statist. 19(2): 817-829 (June, 1991). DOI: 10.1214/aos/1176348122

Abstract

It has been observed that to a smoothing spline operator there corresponds an equivalent kernel operator; these two operators have been compared in a variety of norms [Cox (1984), Silverman (1984)]. In this paper, we refine the existing bounds for the particular case of the spline estimator considered in Rice and Rosenblatt (1983) and its corresponding equivalent kernel estimator. We obtain detailed asymptotic expressions for the bias and covariance functions of the two estimates and provide rates of convergence. Direct comparison then shows that the two estimates are similar. They may differ somewhat in their higher order boundary behavior.

Citation

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K. Messer. "A Comparison of a Spline Estimate to its Equivalent Kernel Estimate." Ann. Statist. 19 (2) 817 - 829, June, 1991. https://doi.org/10.1214/aos/1176348122

Information

Published: June, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0741.62040
MathSciNet: MR1105846
Digital Object Identifier: 10.1214/aos/1176348122

Subjects:
Primary: 62G05
Secondary: 62G20 , 62J02

Keywords: Boundary bias , ‎kernel‎ , Nonparametric regression , Spline

Rights: Copyright © 1991 Institute of Mathematical Statistics

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Vol.19 • No. 2 • June, 1991
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