Open Access
2011 On the asymptotics of penalized spline smoothing
Xiao Wang, Jinglai Shen, David Ruppert
Electron. J. Statist. 5: 1-17 (2011). DOI: 10.1214/10-EJS593


This paper performs an asymptotic analysis of penalized spline estimators. We compare P-splines and splines with a penalty of the type used with smoothing splines. The asymptotic rates of the supremum norm of the difference between these two estimators over compact subsets of the interior and over the entire interval are established. It is shown that a P-spline and a smoothing spline are asymptotically equivalent provided that the number of knots of the P-spline is large enough, and the two estimators have the same equivalent kernels for both interior points and boundary points.


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Xiao Wang. Jinglai Shen. David Ruppert. "On the asymptotics of penalized spline smoothing." Electron. J. Statist. 5 1 - 17, 2011.


Published: 2011
First available in Project Euclid: 14 January 2011

zbMATH: 1274.65012
MathSciNet: MR2763795
Digital Object Identifier: 10.1214/10-EJS593

Primary: 62G08 , 62G20
Secondary: 62G05

Keywords: Boundary kernel , difference penalty , equivalent kernel , Green’s function , P-spline

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

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