The Annals of Statistics

A Comparison of a Spline Estimate to its Equivalent Kernel Estimate

K. Messer

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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.

Article information

Source
Ann. Statist., Volume 19, Number 2 (1991), 817-829.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348122

Digital Object Identifier
doi:10.1214/aos/1176348122

Mathematical Reviews number (MathSciNet)
MR1105846

Zentralblatt MATH identifier
0741.62040

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62G20: Asymptotic properties 62J02: General nonlinear regression

Keywords
Nonparametric regression spline kernel boundary bias

Citation

Messer, K. A Comparison of a Spline Estimate to its Equivalent Kernel Estimate. Ann. Statist. 19 (1991), no. 2, 817--829. doi:10.1214/aos/1176348122. https://projecteuclid.org/euclid.aos/1176348122


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