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.
Publié le : 1984-09-14
Classification:
Nonparametric regression,
variable kernel,
splines,
roughness penalty,
weight function,
adaptive smoothing,
Sobolev space,
penalized maximum likelihood,
curve estimation,
density estimation,
62G05,
62J05,
65D10,
46E35
@article{1176346710,
author = {Silverman, B. W.},
title = {Spline Smoothing: The Equivalent Variable Kernel Method},
journal = {Ann. Statist.},
volume = {12},
number = {1},
year = {1984},
pages = { 898-916},
language = {en},
url = {http://dml.mathdoc.fr/item/1176346710}
}
Silverman, B. W. Spline Smoothing: The Equivalent Variable Kernel Method. Ann. Statist., Tome 12 (1984) no. 1, pp. 898-916. http://gdmltest.u-ga.fr/item/1176346710/