Abstract
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.
Keywords
SmoothingMathematicsSmoothing splineKernel density estimationKernel smootherVariable kernel density estimationNonparametric regressionKernel (algebra)Thin plate splineApplied mathematicsSpline (mechanical)Mathematical optimizationKernel regressionBandwidth (computing)Nonparametric statisticsKernel methodStatisticsComputer scienceSpline interpolationArtificial intelligenceRadial basis function kernelCombinatorics
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Publication Info
- Year
- 1984
- Type
- article
- Volume
- 12
- Issue
- 3
- Citations
- 443
- Access
- Closed
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Cite This
Bernard W. Silverman
(1984).
Spline Smoothing: The Equivalent Variable Kernel Method.
The Annals of Statistics
, 12
(3)
.
https://doi.org/10.1214/aos/1176346710
Identifiers
- DOI
- 10.1214/aos/1176346710