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Stat Sci. 2012;27(4). doi: 10.1214/12-STS392.

A Selective Review of Group Selection in High-Dimensional Models.

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1
Department of Statistics and Actuarial Science, 241 SH, University of Iowa, Iowa City, Iowa 52242, USA.

Abstract

Grouping structures arise naturally in many statistical modeling problems. Several methods have been proposed for variable selection that respect grouping structure in variables. Examples include the group LASSO and several concave group selection methods. In this article, we give a selective review of group selection concerning methodological developments, theoretical properties and computational algorithms. We pay particular attention to group selection methods involving concave penalties. We address both group selection and bi-level selection methods. We describe several applications of these methods in nonparametric additive models, semiparametric regression, seemingly unrelated regressions, genomic data analysis and genome wide association studies. We also highlight some issues that require further study.

KEYWORDS:

Bi-level selection; concave group selection; group LASSO; oracle property; penalized regression; sparsity

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