The Annals of Statistics

Nonparametric regression penalizing deviations from additivity

M. Studer, B. Seifert, and T. Gasser

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 33, Number 3 (2005), 1295-1329.

Dates
First available in Project Euclid: 1 July 2005

Permanent link to this document
https://projecteuclid.org/euclid.aos/1120224103

Digital Object Identifier
doi:10.1214/009053604000001246

Mathematical Reviews number (MathSciNet)
MR2195636

Zentralblatt MATH identifier
1072.62031

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62H99: None of the above, but in this section

Keywords
Nonparametric estimation additive models model choice curse of dimensionality regularization parameter selection AIC

Citation

Studer, M.; Seifert, B.; Gasser, T. Nonparametric regression penalizing deviations from additivity. Ann. Statist. 33 (2005), no. 3, 1295--1329. doi:10.1214/009053604000001246. https://projecteuclid.org/euclid.aos/1120224103


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