A selective review of group selection in high-dimensional models 论文

摘要

Abstract. Grouping structures arise naturally in many statistical modeling problems. Several methods have been proposed for variable selection that re-spect grouping structure in variables. Examples include the group LASSO and several concave group selection methods. In this article, we give a se-lective review of group selection concerning methodological developments, theoretical properties and computational algorithms. We pay particular at-tention to group selection methods involving concave penalties. We address both group selection and bi-level selection methods. We describe several ap-plications of these methods in nonparametric additive models, semiparamet-ric regression, seemingly unrelated regressions, genomic data analysis and genome wide association studies. We also highlight some issues that require further study. Key words and phrases: Bi-level selection, group LASSO, concave group selection, penalized regression, sparsity, oracle property. 1.