Variable selection for semiparametric varying coefficient partially linear models

In this paper, we present a variable selection procedure by combining basis function approximations with SCAD penalty for semiparametric varying coefficient partially linear models. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency of this procedure and the oracle property of the regularized estimators. A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.