We study variable selection for partially linear models when the dimension of covariates diverges with the sample size. We combine the ideas of profiling and adaptive Elastic-Net. The resulting procedure has oracle properties and can handle collinearity well. A by-product is the uniform bound for the absolute difference between the profiled and original predictors. We further examine finite sample performance of the proposed procedure by simulation studies and analysis of a labor-market dataset for an illustration.
Bibliographical noteFunding Information:
Liang's research was partially supported by NSF grant DMS-1007167 .
Copyright 2012 Elsevier B.V., All rights reserved.
- Adaptive regularization
- High dimensionality
- Model selection
- Oracle property
- Semiparametric model
- Shrinkage methods