Open Access
November 2010 Consistent group selection in high-dimensional linear regression
Fengrong Wei, Jian Huang
Bernoulli 16(4): 1369-1384 (November 2010). DOI: 10.3150/10-BEJ252


In regression problems where covariates can be naturally grouped, the group Lasso is an attractive method for variable selection since it respects the grouping structure in the data. We study the selection and estimation properties of the group Lasso in high-dimensional settings when the number of groups exceeds the sample size. We provide sufficient conditions under which the group Lasso selects a model whose dimension is comparable with the underlying model with high probability and is estimation consistent. However, the group Lasso is, in general, not selection consistent and also tends to select groups that are not important in the model. To improve the selection results, we propose an adaptive group Lasso method which is a generalization of the adaptive Lasso and requires an initial estimator. We show that the adaptive group Lasso is consistent in group selection under certain conditions if the group Lasso is used as the initial estimator.


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Fengrong Wei. Jian Huang. "Consistent group selection in high-dimensional linear regression." Bernoulli 16 (4) 1369 - 1384, November 2010.


Published: November 2010
First available in Project Euclid: 18 November 2010

MathSciNet: MR2759183
zbMATH: 1207.62146
Digital Object Identifier: 10.3150/10-BEJ252

Keywords: group selection , High-dimensional data , penalized regression , rate consistency , selection consistency

Rights: Copyright © 2010 Bernoulli Society for Mathematical Statistics and Probability

Vol.16 • No. 4 • November 2010
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