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VARIABLE SELECTION IN NONPARAMETRIC ADDITIVE MODELS (2008)
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BibTeX
@MISC{Huang08variableselection,
author = {Jian Huang and Joel L. Horowitz and Fengrong Wei},
title = {VARIABLE SELECTION IN NONPARAMETRIC ADDITIVE MODELS},
year = {2008}
}
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Abstract
Summary. 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 non-zero additive components is “small” relative to the sample size. The statistical problem is to determine which additive components are non-zero. 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 non-zero components correctly with probability approaching one as the sample size increases and achieves the optimal rate of convergence. Following model selection, oracle-efficient, asymptotically normal estimators of the non-zero components can be obtained by using existing methods. 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. Key words and phrases. Adaptive group Lasso; component selection; highdimensional data; nonparametric regression; selection consistency. Short title. Nonparametric component selection AMS 2000 subject classification. Primary 62G08, 62G20; secondary 62G99 1
Keyphrases
variable selection nonparametric additive model adaptive group lasso additive component sample size component selection non-zero component group lasso monte carlo truncated series expansion statistical problem b-spline base subject classification nonparametric regression model selection conditional mean function short title nonzero component normal estimator optimal rate data example highdimensional data nonparametric component selection am nonparametric additive model moderate size selection consistency sample size increase key word adaptive group lasso procedure non-zero additive component initial estimator
