Journal article
Concave group methods for variable selection and estimation in high-dimensional varying coefficient models
Science China. Mathematics, Vol.57(10), pp.2073-2090
05/30/2014
DOI: 10.1007/s11425-014-4842-y
Abstract
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.
Details
- Title: Subtitle
- Concave group methods for variable selection and estimation in high-dimensional varying coefficient models
- Creators
- GuangRen Yang - Shanghai University of Finance and EconomicsJian Huang - University of IowaYong Zhou - Shanghai University of Finance and Economics
- Resource Type
- Journal article
- Publication Details
- Science China. Mathematics, Vol.57(10), pp.2073-2090
- Publisher
- Science China Press
- DOI
- 10.1007/s11425-014-4842-y
- ISSN
- 1674-7283
- eISSN
- 1869-1862
- Language
- English
- Date published
- 05/30/2014
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9984257621502771
Metrics
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