The Annals of Statistics

Relaxed Boundary Smoothing Splines

Gary W. Oehlert

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Abstract

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.

Article information

Source
Ann. Statist., Volume 20, Number 1 (1992), 146-160.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348516

Digital Object Identifier
doi:10.1214/aos/1176348516

Mathematical Reviews number (MathSciNet)
MR1150338

Zentralblatt MATH identifier
0746.62043

JSTOR
links.jstor.org

Subjects
Primary: 62G07: Density estimation
Secondary: 62G20: Asymptotic properties

Keywords
Splines boundary effects regularization

Citation

Oehlert, Gary W. Relaxed Boundary Smoothing Splines. Ann. Statist. 20 (1992), no. 1, 146--160. doi:10.1214/aos/1176348516. https://projecteuclid.org/euclid.aos/1176348516


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