VARIABLE SELECTION IN NONPARAMETRIC ADDITIVE MODELS

Jian Huang; Joel L Horowitz; Fengrong Wei

doi:10.1214/09-AOS781

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VARIABLE SELECTION IN NONPARAMETRIC ADDITIVE MODELS

Journal article

Open access

Peer reviewed

VARIABLE SELECTION IN NONPARAMETRIC ADDITIVE MODELS

Jian Huang, Joel L Horowitz and Fengrong Wei

Annals of statistics, Vol.38(4), pp.2282-2313

08/01/2010

DOI: 10.1214/09-AOS781

PMCID: PMC2994588

PMID: 21127739

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Abstract

We consider a nonparametric additive model of a conditional mean function in which the number of variables and additive components may be larger than the sample size but the number of nonzero additive components is “small” relative to the sample size. The statistical problem is to determine which additive components are nonzero. The additive components are approximated by truncated series expansions with B-spline bases. With this approximation, the problem of component selection becomes that of selecting the groups of coefficients in the expansion. We apply the adaptive group Lasso to select nonzero components, using the group Lasso to obtain an initial estimator and reduce the dimension of the problem. We give conditions under which the group Lasso selects a model whose number of components is comparable with the underlying model, and the adaptive group Lasso selects the nonzero components correctly with probability approaching one as the sample size increases and achieves the optimal rate of convergence. The results of Monte Carlo experiments show that the adaptive group Lasso procedure works well with samples of moderate size. A data example is used to illustrate the application of the proposed method.

nonparametric regression

Adaptive group Lasso

selection consistency

component selection

high-dimensional data

Details

Title: Subtitle: VARIABLE SELECTION IN NONPARAMETRIC ADDITIVE MODELS
Creators: Jian Huang - Department of Statistics and Actuarial Science, 241 SH, University of Iowa, Iowa City, Iowa 52242, USA
Joel L Horowitz - Department of Economics, Northwestern University, 2001 Sheridan Road, Evanston, Illinois 60208, USA
Fengrong Wei - Department of Mathematics, University of West Georgia, Carrollton, Georgia 30118, USA
Resource Type: Journal article
Publication Details: Annals of statistics, Vol.38(4), pp.2282-2313
DOI: 10.1214/09-AOS781
PMID: 21127739
PMCID: PMC2994588
ISSN: 0090-5364
eISSN: 2168-8966
Language: English
Date published: 08/01/2010
Academic Unit: Statistics and Actuarial Science
Record Identifier: 9983985916002771

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