The Annals of Statistics

Bandwidth selection for smooth backfitting in additive models

Enno Mammen and Byeong U. Park

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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.

Article information

Ann. Statist., Volume 33, Number 3 (2005), 1260-1294.

First available in Project Euclid: 1 July 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G07: Density estimation
Secondary: 62G20: Asymptotic properties

Backfitting bandwidth selection penalized least squares plug-in rules nonparametric regression Nadaraya–Watson local polynomial smoothing


Mammen, Enno; Park, Byeong U. Bandwidth selection for smooth backfitting in additive models. Ann. Statist. 33 (2005), no. 3, 1260--1294. doi:10.1214/009053605000000101.

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