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June 2005 Bandwidth selection for smooth backfitting in additive models
Enno Mammen, Byeong U. Park
Ann. Statist. 33(3): 1260-1294 (June 2005). DOI: 10.1214/009053605000000101


The smooth backfitting introduced by Mammen, Linton and Nielsen [Ann. Statist. 27 (1999) 1443–1490] is a promising technique to fit additive regression models and is known to achieve the oracle efficiency bound. In this paper, we propose and discuss three fully automated bandwidth selection methods for smooth backfitting in additive models. The first one is a penalized least squares approach which is based on higher-order stochastic expansions for the residual sums of squares of the smooth backfitting estimates. The other two are plug-in bandwidth selectors which rely on approximations of the average squared errors and whose utility is restricted to local linear fitting. The large sample properties of these bandwidth selection methods are given. Their finite sample properties are also compared through simulation experiments.


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Enno Mammen. Byeong U. Park. "Bandwidth selection for smooth backfitting in additive models." Ann. Statist. 33 (3) 1260 - 1294, June 2005.


Published: June 2005
First available in Project Euclid: 1 July 2005

zbMATH: 1072.62025
MathSciNet: MR2195635
Digital Object Identifier: 10.1214/009053605000000101

Primary: 62G07
Secondary: 62G20

Keywords: backfitting , Bandwidth selection , local polynomial smoothing , Nadaraya–Watson , Nonparametric regression , penalized least squares , plug-in rules

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 3 • June 2005
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