The Annals of Statistics
- Ann. Statist.
- Volume 12, Number 3 (1984), 898-916.
Spline Smoothing: The Equivalent Variable Kernel Method
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.
Ann. Statist., Volume 12, Number 3 (1984), 898-916.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G05: Estimation
Secondary: 62J05: Linear regression 65D10: Smoothing, curve fitting 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems
Silverman, B. W. Spline Smoothing: The Equivalent Variable Kernel Method. Ann. Statist. 12 (1984), no. 3, 898--916. doi:10.1214/aos/1176346710. https://projecteuclid.org/euclid.aos/1176346710