Variable selection for generalized varying coefficient partially linear models with diverging number of parameters

Semiparametric models with diverging number of predictors arise in many contemporary scientific areas. Variable selection for these models consists of two components: model selection for non-parametric components and selection of significant variables for the parametric portion. In this paper, we consider a variable selection procedure by combining basis function approximation with SCAD penalty. The proposed procedure simultaneously selects significant variables in the parametric components and the nonparametric components. With appropriate selection of tuning parameters, we establish the consistency and sparseness of this procedure.