Feature Selection for Varying Coefficient Models With Ultrahigh Dimensional Covariates
Jingyuan Liu
Wang Yanan Institute for Studies in Economics, Xiamen University
Runze Li
Rongling Wu
11/3/2013 7:37:50 PM
This paper is concerned with feature screening and variable selection for varying coefficient models with ultrahigh dimensional covariates. We propose a new feature screening procedure for these models based on conditional correlation coefficient. We systematically study the theoretical properties of the proposed procedure, and estab- lish their sure screening property and the ranking consistency. To enhance the finite sample performance of the proposed procedure, we further develop an iterative feature screening procedure. Monte Carlo simulation studies were conducted to examine the performance of the proposed procedures. In practice, we advocate a two-stage approach for varying coefficient models. The two stage approach consists of (a) reducing the ultrahigh dimensionality by using the proposed procedure and (b) applying regularization methods for dimension-reduced varying coefficient models to make statistical inferences on the coefficient functions. We illustrate the proposed two-stage approach by a real data example.
Feature selection, varying coefficient models, ranking consistency, sure screen- ing property