THE Mnet method for variable selection

Jian Huang, Patrick Breheny, Sangin Lee, Shuangge Ma, Cun Hui Zhang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

17 Citations (Scopus)

Abstract

We propose a penalized approach for variable selection using a combination of minimax concave and ridge penalties. The method is designed to deal with p ≥ n problems with highly correlated predictors. We call this the Mnet method. Similar to the elastic net of Zou and Hastie (2005), the Mnet tends to select or drop highly correlated predictors together. However, unlike the elastic net, the Mnet is selection consistent and equal to the oracle ridge estimator with high probability under reasonable conditions. We develop an efficient coordinate descent algorithm to compute the Mnet estimates. Simulation studies show that the Mnet has better performance in the presence of highly correlated predictors than either the elastic net or MCP. We illustrate the application of the Mnet to data from a gene expression study in ophthalmology.

Original languageEnglish
Pages (from-to)903-923
Number of pages21
JournalStatistica Sinica
Volume26
Issue number3
DOIs
Publication statusPublished - 1 Jul 2016
Externally publishedYes

Keywords

  • Correlated predictors
  • Minimax concave penalty
  • Oracle property
  • P < n problems
  • Ridge regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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