Consistent group selection in high-dimensional linear regression

FENGRONG WEI; JIAN HUANG

doi:10.3150/10-BEJ252

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Consistent group selection in high-dimensional linear regression

Journal article

Open access

Peer reviewed

Consistent group selection in high-dimensional linear regression

FENGRONG WEI and JIAN HUANG

Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, Vol.16(4), pp.1369-1384

11/2010

DOI: 10.3150/10-BEJ252

PMCID: PMC3209717

PMID: 22072891

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Abstract

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.

group selection

rate consistency

penalized regression

selection consistency

high-dimensional data

Details

Title: Subtitle: Consistent group selection in high-dimensional linear regression
Creators: FENGRONG WEI - Department of Statistics and Actuarial Science, University of Iowa, Iowa City, IA 52242, USA
JIAN HUANG - Department of Statistics and Actuarial Science, University of Iowa, Iowa City, IA 52242, USA
Resource Type: Journal article
Publication Details: Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, Vol.16(4), pp.1369-1384
DOI: 10.3150/10-BEJ252
PMID: 22072891
PMCID: PMC3209717
ISSN: 1350-7265
eISSN: 1573-9759
Grant note: R01 CA120988-03 || CA / National Cancer Institute : NCI
Language: English
Date published: 11/2010
Academic Unit: Statistics and Actuarial Science
Record Identifier: 9983985825702771

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