Forward Selection for Feature Screening and Structure Identification in Varying Coefficient Models

Varying coefficient models have flexibility and interpretability, and they are widely used in data analysis. Although feature screening procedures have been proposed for ultra-high dimensional varying coefficient models, none of these procedures includes structure identification. That is, existing feature screening procedures for varying coefficient models do not give us information on which covariates have constant coefficients and which covariates have non-constant coefficients among selected covariates. Hence, these procedures do not explicitly select partially linear varying coefficient models, which are much simpler than general varying coefficient models. Motivated by this issue, we propose a forward selection procedure for simultaneous feature screening and structure identification in varying coefficient models. Unlike existing feature screening procedures, our method classifies all covariates into three groups: covariates with constant coefficients, covariates with non-constant coefficients, and covariates with zero coefficients. Thus, our procedure can explicitly select partially linear varying coefficient models. Our procedure selects covariates sequentially until the extended BIC (EBIC) increases. We establish the screening consistency for our method under some conditions. Numerical studies and real data examples support the utility of our procedure.