title: Feature Selection for Varying Coefficient Models With Ultrahigh Dimensional Covariates.
abstract: 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 establish 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.
authors.affiliation: Assistant Professor of Wang Yanan Institute for Studies in Economics and Department of Statistics and Fujian Key Laboratory of Statistical Science, Xiamen University, China.
authors.forename: Jingyuan
authors.initials: J
authors.lastname: Liu
authors.affiliation: Distinguished Professor, Department of Statistics and The Methodology Center, The Pennsylvania State University, University Park, PA 16802-2111.
authors.forename: Runze
authors.initials: R
authors.lastname: Li
authors.affiliation: Professor, Department of Public Health Sciences, Penn State Hershey College of Medicine, Hershey, PA 17033.
authors.forename: Rongling
authors.initials: R
authors.lastname: Wu
keywords: Feature selection; ranking consistency; sure screening property; varying coefficient models