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Cited by 441

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 access
Silverman, B. W.·1984·The Annals of Statistics

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.

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Crossref · 10.1214/aos/1176346710

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Metadata

Authors
Silverman, B. W.
Venue
The Annals of 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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