Open Access
March, 1992 Relaxed Boundary Smoothing Splines
Gary W. Oehlert
Ann. Statist. 20(1): 146-160 (March, 1992). DOI: 10.1214/aos/1176348516


Ordinary smoothing splines have an integrated mean squared error which is dominated by bias contributions at the boundaries. When the estimated function has additional derivatives, the boundary contribution to the bias affects the asymptotic rate of convergence unless the derivatives of the estimated function meet the natural boundary conditions. This paper introduces relaxed boundary smoothing splines and shows that they obtain the optimal asymptotic rate of convergence without conditions on the boundary derivatives of the estimated function.


Download Citation

Gary W. Oehlert. "Relaxed Boundary Smoothing Splines." Ann. Statist. 20 (1) 146 - 160, March, 1992.


Published: March, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0746.62043
MathSciNet: MR1150338
Digital Object Identifier: 10.1214/aos/1176348516

Primary: 62G07
Secondary: 62G20

Keywords: boundary effects , regularization , splines

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 1 • March, 1992
Back to Top