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June, 1983 Asymptotics for $M$-Type Smoothing Splines
Dennis D. Cox
Ann. Statist. 11(2): 530-551 (June, 1983). DOI: 10.1214/aos/1176346159

Abstract

Limit theorems giving rates of convergence of nonparametric regression estimates obtained from smoothing splines are proved. The main emphasis is on nonlinear, robust smoothing splines, but new results are obtained for the usual (linear) case. It is assumed that the knots become asymptotically uniform in a vague sense. Convergence of derivatives is also investigated. The main mathematical tools are a linearization of the robust smoothing spline, and an approximation of the linear smoothing spline utilizing the Green's function of an associated boundary value problem.

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Dennis D. Cox. "Asymptotics for $M$-Type Smoothing Splines." Ann. Statist. 11 (2) 530 - 551, June, 1983. https://doi.org/10.1214/aos/1176346159

Information

Published: June, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0519.62034
MathSciNet: MR696065
Digital Object Identifier: 10.1214/aos/1176346159

Subjects:
Primary: 62J99
Secondary: 41A15, 62F35, 62G05

Rights: Copyright © 1983 Institute of Mathematical Statistics

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Vol.11 • No. 2 • June, 1983
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