Concave group methods for variable selection and estimation in high-dimensional varying coefficient models  

作　　者：YANG GuangRen HUANG Jian ZHOU Yong 

机构地区：[1]Department of Statistics,School of Economics,Jinan University [2]School of Statistics and Management,Shanghai University of Finance and Economics [3]Department of Statistics and Actuarial Science,University of Iowa [4]Academy of Mathematics and Systems Science,Chinese Academy of Sciences

出　　处：《Science China Mathematics》2014年第10期2073-2090,共18页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(GrantNos.71271128 and 11101442);the State Key Program of National Natural Science Foundation of China(GrantNo.71331006);National Center for Mathematics and Interdisciplinary Sciences(NCMIS);Shanghai Leading Academic Discipline Project A,in Ranking Top of Shanghai University of Finance and Economics(IRTSHUFE);Scientific Research Innovation Fund for PhD Studies(Grant No.CXJJ-2011-434)

摘　　要：The varying-coefficient model is flexible and powerful for modeling the dynamic changes of regression coefficients. We study the problem of variable selection and estimation in this model in the sparse, high- dimensional case. We develop a concave group selection approach for this problem using basis function expansion and study its theoretical and empirical properties. We also apply the group Lasso for variable selection and estimation in this model and study its properties. Under appropriate conditions, we show that the group least absolute shrinkage and selection operator （Lasso） selects a model whose dimension is comparable to the underlying mode], regardless of the large number of unimportant variables. In order to improve the selection results, we show that the group minimax concave penalty （MCP） has the oracle selection property in the sense that it correctly selects important variables with probability converging to one under suitable conditions. By comparison, the group Lasso does not have the oracle selection property. In the simulation parts, we apply the group Lasso and the group MCP. At the same time, the two approaches are evaluated using simulation and demonstrated on a data example.The varying-coefficient model is flexible and powerful for modeling the dynamic changes of regression coefficients.We study the problem of variable selection and estimation in this model in the sparse,highdimensional case.We develop a concave group selection approach for this problem using basis function expansion and study its theoretical and empirical properties.We also apply the group Lasso for variable selection and estimation in this model and study its properties.Under appropriate conditions,we show that the group least absolute shrinkage and selection operator(Lasso)selects a model whose dimension is comparable to the underlying model,regardless of the large number of unimportant variables.In order to improve the selection results,we show that the group minimax concave penalty(MCP)has the oracle selection property in the sense that it correctly selects important variables with probability converging to one under suitable conditions.By comparison,the group Lasso does not have the oracle selection property.In the simulation parts,we apply the group Lasso and the group MCP.At the same time,the two approaches are evaluated using simulation and demonstrated on a data example.

关 键 词：basis expansion group lasso group MCP high-dimensional data SPARSITY oracle property 

分 类 号：O212.4[理学—概率论与数理统计]