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November 2012 A Selective Review of Group Selection in High-Dimensional Models
Jian Huang, Patrick Breheny, Shuangge Ma
Statist. Sci. 27(4): 481-499 (November 2012). DOI: 10.1214/12-STS392


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.


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Jian Huang. Patrick Breheny. Shuangge Ma. "A Selective Review of Group Selection in High-Dimensional Models." Statist. Sci. 27 (4) 481 - 499, November 2012.


Published: November 2012
First available in Project Euclid: 21 December 2012

zbMATH: 1331.62347
MathSciNet: MR3025130
Digital Object Identifier: 10.1214/12-STS392

Keywords: Bi-level selection , concave group selection , group lasso , oracle property , penalized regression , Sparsity

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.27 • No. 4 • November 2012
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