Semiparametric regression models with multiple covariates are commonly encountered. When there are covariates that are not associated with a response variable, variable selection may lead to sparser models, more lucid interpretations and more accurate estimation. In this study, we adopt a sieve approach for the estimation of nonparametric covariate effects in semiparametric regression models. We adopt a two-step iterated penalisation approach for variable selection. In the first step, a mixture of Lasso and group Lasso penalties are employed to conduct the first-round variable selection and obtain the initial estimate. In the second step, a mixture of weighted Lasso and weighted group Lasso penalties, with weights constructed using the initial estimate, are employed for variable selection. We show that the proposed iterated approach has the variable selection consistency property, even when the number of unknown parameters diverges with sample size. Numerical studies, including simulation and analysis of a diabetes data set, show satisfactory performance of the proposed approach.

中文翻译：

---

具有迭代惩罚的半参数回归模型的变量选择

通常会遇到具有多个协变量的半参数回归模型。当存在与响应变量无关的协变量时，变量选择可能会导致模型更稀疏、解释更清晰和估计更准确。在这项研究中，我们采用筛选方法来估计半参数回归模型中的非参数协变量效应。我们采用两步迭代惩罚方法进行变量选择。在第一步中，采用 Lasso 和 Group Lasso 惩罚的混合进行第一轮变量选择并获得初始估计。在第二步中，加权 Lasso 和加权组 Lasso 惩罚的混合，使用初始估计构建权重，用于变量选择。我们表明，即使未知参数的数量随着样本大小而发散，所提出的迭代方法也具有变量选择的一致性属性。数值研究，包括对糖尿病数据集的模拟和分析，显示了所提出方法的令人满意的性能。