A group adaptive elastic-net approach for variable selection in high-dimensional linear regression

Jianhua Hu, Jian Huang, Feng Qiu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)

Abstract

In practice, predictors possess grouping structures spontaneously. Incorporation of such useful information can improve statistical modeling and inference. In addition, the high-dimensionality often leads to the collinearity problem. The elastic net is an ideal method which is inclined to reflect a grouping effect. In this paper, we consider the problem of group selection and estimation in the sparse linear regression model in which predictors can be grouped. We investigate a group adaptive elastic-net and derive oracle inequalities and model consistency for the cases where group number is larger than the sample size. Oracle property is addressed for the case of the fixed group number. We revise the locally approximated coordinate descent algorithm to make our computation. Simulation and real data studies indicate that the group adaptive elastic-net is an alternative and competitive method for model selection of high-dimensional problems for the cases of group number being larger than the sample size.

Original languageEnglish
Pages (from-to)173-188
Number of pages16
JournalScience China Mathematics
Volume61
Issue number1
DOIs
Publication statusPublished - 1 Jan 2018
Externally publishedYes

Keywords

  • group adaptive elastic-net
  • group variable selection
  • high-dimensional regression
  • oracle inequalities
  • oracle property

ASJC Scopus subject areas

  • Mathematics(all)

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