A Unified Approach to Variable Selection for Partially Linear Models

Abstract

We focus on the general partially linear model without any structure assumption on the nonparametric component. For such a model with both linear and nonlinear predictors being multivariate, we propose a new variable selection method. Our new method is a unified approach in the sense that it can select both linear and nonlinear predictors simultaneously by solving a single optimization problem. We prove that the proposed method achieves consistency. Both simulation examples and a real data example are used to demonstrate the new method’s competitive finite-sample performance. Supplementary materials for this article are available online.

Keywords:

• Partially linear model
• Profile-kernel estimation
• Variable selection

Acknowledgments

The authors thank the coeditor, an associate editor, and two reviewers for their constructive suggestions and comments that lead to substantial improvements in the article.

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

Wu’s research is partially supported by National Institutes of Health grant RF1MH125928 and National Science Foundation grants DMS-2152070 and CCF-2216912.