A Unified Variable Selection Method for (Generalized) Partially Linear Models

We focus on the 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. We also extend this framework to generalized partially linear models.