A Unified Approach to Variable Selection for Partially Linear Models

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.

本文聚焦于非参数分量无任何结构假设的一般部分线性模型。针对此类同时包含多元线性预测变量与非线性预测变量的模型，本文提出一种全新的变量选择方法。该方法属于统一求解框架，仅需求解单个优化问题，即可同时完成线性与非线性预测变量的变量筛选。本文证明了所提方法具备相合性。通过仿真实验与真实数据集案例，验证了所提方法具有颇具竞争力的有限样本性能。本文的补充材料可在线获取。