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September, 1984 Spline Smoothing: The Equivalent Variable Kernel Method
B. W. Silverman
Ann. Statist. 12(3): 898-916 (September, 1984). DOI: 10.1214/aos/1176346710


The spline smoothing approach to nonparametric regression and curve estimation is considered. It is shown that, in a certain sense, spline smoothing corresponds approximately to smoothing by a kernel method with bandwidth depending on the local density of design points. Some exact calculations demonstrate that the approximation is extremely close in practice. Consideration of kernel smoothing methods demonstrates that the way in which the effective local bandwidth behaves in spline smoothing has desirable properties. Finally, the main result of the paper is applied to the related topic of penalized maximum likelihood probability density estimates; a heuristic discussion shows that these estimates should adapt well in the tails of the distribution.


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B. W. Silverman. "Spline Smoothing: The Equivalent Variable Kernel Method." Ann. Statist. 12 (3) 898 - 916, September, 1984.


Published: September, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0547.62024
MathSciNet: MR751281
Digital Object Identifier: 10.1214/aos/1176346710

Primary: 62G05
Secondary: 46E35, 62J05, 65D10

Rights: Copyright © 1984 Institute of Mathematical Statistics


Vol.12 • No. 3 • September, 1984
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