Bernoulli

  • Bernoulli
  • Volume 5, Number 2 (1999), 359-379.

Derivation of equivalent kernel for general spline smoothing: a systematic approach

Felix Abramovich and Vadim Grinshtein

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Abstract

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.

Article information

Source
Bernoulli, Volume 5, Number 2 (1999), 359-379.

Dates
First available in Project Euclid: 5 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1173147911

Mathematical Reviews number (MathSciNet)
MR1681703

Zentralblatt MATH identifier
0954.62045

Keywords
Green's function L-smoothing spline

Citation

Abramovich, Felix; Grinshtein, Vadim. Derivation of equivalent kernel for general spline smoothing: a systematic approach. Bernoulli 5 (1999), no. 2, 359--379. https://projecteuclid.org/euclid.bj/1173147911


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