Electronic Journal of Statistics

On the asymptotics of penalized spline smoothing

Xiao Wang, Jinglai Shen, and David Ruppert

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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.

Article information

Electron. J. Statist., Volume 5 (2011), 1-17.

First available in Project Euclid: 14 January 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression 62G20: Asymptotic properties
Secondary: 62G05: Estimation

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


Wang, Xiao; Shen, Jinglai; Ruppert, David. On the asymptotics of penalized spline smoothing. Electron. J. Statist. 5 (2011), 1--17. doi:10.1214/10-EJS593. https://projecteuclid.org/euclid.ejs/1295040628

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