Single-index varying-coefficient models include many types of popular semiparametric models, i.e., single-index models, partially linear models, varying coefficient models, and so on. In this paper, a two-stage efficient variable selection procedure is proposed to select important nonparametric and parametric components and obtain estimators simultaneously. We also find that the proposed procedure can separate predictors into varying-coefficient and constant-coefficient predictors automatically. Theoretically, it has the selection and estimation consistency properties. Simulation studies and a real data application are conducted to evaluate and illustrate the proposed methods.

中文翻译：

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单指标变系数模型的模型识别与选择

单指数变系数模型包括多种流行的半参数模型，即单指数模型、部分线性模型、变系数模型等。在本文中，提出了一种两阶段有效的变量选择程序来选择重要的非参数和参数分量并同时获得估计量。我们还发现所提出的程序可以自动将预测变量分为变系数和常数系数预测变量。理论上，它具有选择和估计一致性的特性。进行模拟研究和实际数据应用以评估和说明所提出的方法。