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

作     者：Yue Yong SHI Yu Ling JIAO Yong Xiu CAO Yan Yan LIU 

作者机构：School of Economics and Management China University of Geosciences Wuhan 430074 P. R. China Center for Resources and Environmental Economic Research China University of Geosciences Wuhan 430074 P. R. China School of Statistics and Mathematics Zhongnan University of Economics and Law Wuhan 430073 P. R. China School of Mathematics and Statistics Wuhan University Wuhan 430072 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2018年第34卷第12期

页      面：1892-1906页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 080901[工学-物理电子学] 0809[工学-电子科学与技术（可授工学、理学学位）] 08[工学] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China(Grant Nos.11571263,11501579,11701571 and41572315) the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(Grant No.CUGW150809) 

主　　题：Alternating direction method of multipliers coordinate descent continuation high-dimen-sional BIC minimax concave penalty penalized least squares 

摘      要：The minimax concave penalty （MCP） has been demonstrated theoretically and practical- ly 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 con- ditions 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.