Abstract: Nonparametric varying coefficient models are useful for the analysis of repeated measurements. While many procedures have been developed for estimating varying-coefficients, there have been few results on variable selection for such models. Recently, Wang, Chen and Li (2007) proposed a group SCAD procedure for model selection in varying-coefficient models, and Wang, Li and Huang (2008) established the existence of a local minimizer of the group SCAD criterion that has the oracle property. However, whether the final estimator from the gSCAD procedure via local quadratic approximation always finds the desired local minimizer is not clear. In this paper, by linearizing the gSCAD penalty we propose a one-step estimator that has the oracle property in variable selection and estimation. The proposed estimator has a much simpler implementation and gives better performance in variable selection and estimation than the ordinary gSCAD estimator.
Key words and phrases: One-step gSCAD, oracle property, spline basis, variable selection, varying-coefficient.