The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Spline Smoothing: The Equivalent Variable Kernel Method
Open accessAbstract
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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Citations
Cites
Craven, P., & Wahba, G. (1978) · Numerische Mathematik · doi:10.1007/bf01404567 · Cited by 3,388
Cited by
Gaussian Processes for Machine Learning
Rasmussen, C. E., & Williams, C. K. I. (2005) · doi:10.7551/mitpress/3206.001.0001 · Cited by 11,705
“h(x∗) is called the weight function [Silverman, 1984].”
Some aspects of the spline smoothing approach to non-parametric regression curve fitting
Silverman, B. W. (1985) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1985.tb01327.x · Cited by 1,117
Self-citationMaximum entropy autoregressive conditional heteroskedasticity model
Park, S. Y., & Bera, A. K. (2009) · Journal of Econometrics · doi:10.1016/j.jeconom.2008.12.014 · Cited by 218
Metadata
- Authors
- Silverman, B. W.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1984-09-01
- Volume
- 12
- Issue
- 3
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W1965999112
- Cited by
- 441
- References
- 1
- FWCI
- 3.49
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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