Feature Selection for Varying Coefficient Models With Ultrahigh-Dimensional Covariates

Abstract

This article 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. Supplementary materials for this article are available online.

KEY WORDS:

• Conditional correlation
• Ranking consistency
• Sure screening property
• Ultrahigh dimensionality
• Varying coefficient models

Additional information

Funding

The research of Runze Li was supported by National Institute on Drug Abuse (NIDA) grant P50-DA10075, National Cancer Institute (NCI) grant R01 CA168676, and National Natural Science Foundation of China grant 11028103. The research of Rongling Wu was supported by an NSF grant IOS-0923975 and an NIH grant UL1RR0330184. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NSF, NIH, NIDA, and NCI.