Consistent group identification and variable selection in regression with correlated predictors

Dhruv B. Sharma, Howard D. Bondell, Hao Zhang

Research output: Contribution to journalArticle

13 Scopus citations

Abstract

Statistical procedures for variable selection have become integral elements in any analysis. Successful procedures are characterized by high predictive accuracy, yielding interpretable models while retaining computational efficiency. Penalized methods that perform coefficient shrinkage have been shown to be successful in many cases. Models with correlated predictors are particularly challenging to tackle. We propose a penalization procedure that performs variable selection while clustering groups of predictors automatically. The oracle properties of this procedure, including consistency in group identification, are also studied. The proposed method compares favorably with existing selection approaches in both prediction accuracy and model discovery, while retaining its computational efficiency. Supplementary materials are available online.

Original languageEnglish (US)
Pages (from-to)319-340
Number of pages22
JournalJournal of Computational and Graphical Statistics
Volume22
Issue number2
DOIs
Publication statusPublished - 2013
Externally publishedYes

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Keywords

  • Coefficient shrinkage
  • Correlation
  • Oracle properties
  • Penalization
  • Structure identification
  • Supervised clustering

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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