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april 1999 Derivation of equivalent kernel for general spline smoothing: a systematic approach
Felix Abramovich, Vadim Grinshtein
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Bernoulli 5(2): 359-379 (april 1999).


We consider first the spline smoothing nonparametric estimation with variable smoothing parameter and arbitrary design density function and show that the corresponding equivalent kernel can be approximated by the Green function of a certain linear differential operator. Furthermore, we propose to use the standard (in applied mathematics and engineering) method for asymptotic solution of linear differential equations, known as the Wentzel-Kramers-Brillouin method, for systematic derivation of an asymptotically equivalent kernel in this general case. The corresponding results for polynomial splines are a special case of the general solution. Then, we show how these ideas can be directly extended to the very general L-spline smoothing.


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Felix Abramovich. Vadim Grinshtein. "Derivation of equivalent kernel for general spline smoothing: a systematic approach." Bernoulli 5 (2) 359 - 379, april 1999.


Published: april 1999
First available in Project Euclid: 5 March 2007

zbMATH: 0954.62045
MathSciNet: MR1681703

Keywords: Green's function , L-smoothing spline

Rights: Copyright © 1999 Bernoulli Society for Mathematical Statistics and Probability


Vol.5 • No. 2 • april 1999
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