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Acta Mathematica Sinica, English Series

, Volume 34, Issue 12, pp 1892–1906 | Cite as

An Alternating Direction Method of Multipliers for MCP-penalized Regression with High-dimensional Data

  • Yue Yong Shi
  • Yu Ling Jiao
  • Yong Xiu Cao
  • Yan Yan LiuEmail author
Article
  • 105 Downloads

Abstract

The minimax concave penalty (MCP) has been demonstrated theoretically and practically to be effective in nonconvex penalization for variable selection and parameter estimation. In this paper, we develop an efficient alternating direction method of multipliers (ADMM) with continuation algorithm for solving the MCP-penalized least squares problem in high dimensions. Under some mild conditions, we study the convergence properties and the Karush–Kuhn–Tucker (KKT) optimality conditions of the proposed method. A high-dimensional BIC is developed to select the optimal tuning parameters. Simulations and a real data example are presented to illustrate the efficiency and accuracy of the proposed method.

Keywords

Alternating direction method of multipliers coordinate descent continuation high-dimensional BIC minimax concave penalty penalized least squares 

MR(2010) Subject Classification

62J05 62J07 62J99 

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Notes

Acknowledgements

The authors sincerely thank the associate editor and the referees for their valuable comments and suggestions that have led to significant improvement of this article.

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Yue Yong Shi
    • 1
    • 2
  • Yu Ling Jiao
    • 3
  • Yong Xiu Cao
    • 3
  • Yan Yan Liu
    • 4
    Email author
  1. 1.School of Economics and ManagementChina University of GeosciencesWuhanP. R. China
  2. 2.Center for Resources and Environmental Economic ResearchChina University of GeosciencesWuhanP. R. China
  3. 3.School of Statistics and MathematicsZhongnan University of Economics and LawWuhanP. R. China
  4. 4.School of Mathematics and StatisticsWuhan UniversityWuhanP. R. China

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