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June 2005 Nonparametric regression penalizing deviations from additivity
M. Studer, B. Seifert, T. Gasser
Ann. Statist. 33(3): 1295-1329 (June 2005). DOI: 10.1214/009053604000001246

Abstract

Due to the curse of dimensionality, estimation in a multidimensional nonparametric regression model is in general not feasible. Hence, additional restrictions are introduced, and the additive model takes a prominent place. The restrictions imposed can lead to serious bias. Here, a new estimator is proposed which allows penalizing the nonadditive part of a regression function. This offers a smooth choice between the full and the additive model. As a byproduct, this penalty leads to a regularization in sparse regions. If the additive model does not hold, a small penalty introduces an additional bias compared to the full model which is compensated by the reduced bias due to using smaller bandwidths.

For increasing penalties, this estimator converges to the additive smooth backfitting estimator of Mammen, Linton and Nielsen [Ann. Statist. 27 (1999) 1443–1490].

The structure of the estimator is investigated and two algorithms are provided. A proposal for selection of tuning parameters is made and the respective properties are studied. Finally, a finite sample evaluation is performed for simulated and ozone data.

Citation

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M. Studer. B. Seifert. T. Gasser. "Nonparametric regression penalizing deviations from additivity." Ann. Statist. 33 (3) 1295 - 1329, June 2005. https://doi.org/10.1214/009053604000001246

Information

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

zbMATH: 1072.62031
MathSciNet: MR2195636
Digital Object Identifier: 10.1214/009053604000001246

Subjects:
Primary: 62G08
Secondary: 62H99

Keywords: Additive models , AIC , curse of dimensionality , model choice , nonparametric estimation , parameter selection , regularization

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 3 • June 2005
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