TY - JOUR
T1 - Concave group methods for variable selection and estimation in high-dimensional varying coefficient models
AU - Yang, Guang Ren
AU - Huang, Jian
AU - Zhou, Yong
N1 - Funding Information:
Acknowledgements This work was supported by National Natural Science Foundation of China (Grant Nos. 71271128 and 11101442), the State Key Program of National Natural Science Foundation of China (Grant No. 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) and Scientific Research Innovation Fund for PhD Studies (Grant No. CXJJ-2011-434).
PY - 2014/10
Y1 - 2014/10
N2 - 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 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.
AB - 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 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.
UR - http://www.scopus.com/inward/record.url?scp=84906081649&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84906081649&partnerID=8YFLogxK
U2 - 10.1007/s11425-014-4842-y
DO - 10.1007/s11425-014-4842-y
M3 - Article
AN - SCOPUS:84906081649
SN - 1674-7283
VL - 57
SP - 2073
EP - 2090
JO - Science China Mathematics
JF - Science China Mathematics
IS - 10
ER -