The Annals of Statistics

Smoothing Splines: Regression, Derivatives and Deconvolution

John Rice and Murray Rosenblatt

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Abstract

The statistical properties of a cubic smoothing spline and its derivative are analyzed. It is shown that unless unnatural boundary conditions hold, the integrated squared bias is dominated by local effects near the boundary. Similar effects are shown to occur in the regularized solution of a translation-kernel integral equation. These results are derived by developing a Fourier representation for a smoothing spline.

Article information

Source
Ann. Statist., Volume 11, Number 1 (1983), 141-156.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346065

Digital Object Identifier
doi:10.1214/aos/1176346065

Mathematical Reviews number (MathSciNet)
MR684872

Zentralblatt MATH identifier
0535.41019

JSTOR
links.jstor.org

Subjects
Primary: 62G99: None of the above, but in this section
Secondary: 62J99: None of the above, but in this section 41A15: Spline approximation

Keywords
Spline smoothing spline regularization deconvolution

Citation

Rice, John; Rosenblatt, Murray. Smoothing Splines: Regression, Derivatives and Deconvolution. Ann. Statist. 11 (1983), no. 1, 141--156. doi:10.1214/aos/1176346065. https://projecteuclid.org/euclid.aos/1176346065


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