Derivation of equivalent kernel for general spline smoothing: A system approach
type: Item
instance of: scholarly article
title: Derivation of equivalent kernel for general spline smoothing: A system approach
zbMATH Open document ID: 0954.62045
DOI: 10.2307/3318440
author: Vadim Grinshtein
author: Felix P. Abramovich
published in: Bernoulli
publication date: 2001-01-28T00:00:00Z
review text: Spline smoothing for estimating regression functions is considered. The authors extend results about equivalent kernels in two directions -- arbitrary design densities and variable smoothing parameters are included. It is shown that also in this more general case the equivalent kernels can be approximated by the Green functions of certain linear differential operators. A standard method, known as the Wentzel-Kramers-Brillouin method, for the systematic derivation of asymptotically equivalent kernels is proposed. Furthermore, the problem of finding equivalent kernels for general \(L\)-spline smoothing is considered.
Mathematics Subject Classification ID: 62G08
Mathematics Subject Classification ID: 62G20
zbMATH DE Number: 1294465
zbMATH Keywords: Green's function
zbMATH Keywords: L-smoothing spline
zbMATH Keywords: variable smoothing parameter
zbMATH Keywords: Wentzel-Kramers-Brillouin method
reviewed by: Hannelore Liero
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/3318440
OpenAlex ID: W1993110523
description: scientific article; zbMATH DE number 1294465