Feature Selection for High-Dimensional Varying Coefficient Models via Ordinary Least Squares Projection

Feature selection is a changing issue for varying coefficient models when the dimensionality of covariates is ultrahigh. The traditional technology of significantly reducing dimensionality is the marginal correlation screening method based on nonparametric smoothing. However, marginal correlation screening methods may be screen out variables that are jointly correlated to the response. To address this, we propose a novel screener with the name of group screening via nonparametric smoothing high-dimensional ordinary least squares projection, referred to as "Group HOLP" and study its sure screening property. Based on this nice property, we introduce a refined feature selection procedure via employing the extended Bayesian information criteria (EBIC) to select the suitable submodels in varying coefficient models, which is coined as Group HOLP-EBIC method. Under some regularity conditions, we establish the strong consistency of feature selection for the proposed method. The performance of our method is evaluated by simulations and further illustrated by two real examples.