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Nonparametric regression penalizing deviations from additivity


Studer, M; Seifert, Burkhardt; Gasser, Theo (2005). Nonparametric regression penalizing deviations from additivity. Annals of Statistics, 33(3):1295-1329.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:04 Faculty of Medicine > Epidemiology, Biostatistics and Prevention Institute (EBPI)
Dewey Decimal Classification:610 Medicine & health
Language:English
Date:2005
Deposited On:10 Jun 2009 13:19
Last Modified:19 Feb 2018 19:56
Publisher:Institute of Mathematical Statistics
ISSN:0090-5364
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1214/009053604000001246
Related URLs:http://e-collection.ethbib.ethz.ch/eserv/eth:25957/eth-25957-01.pdf (Organisation)
http://www.biostat.uzh.ch/research/software/nonaddpenalty.html (Organisation)
http://arxiv.org/abs/math/0507426 (Organisation)

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