This paper focuses on variable selection for a partially linear single-index varying-coefficient model. A regularized variable selection procedure by combining basis function approximations with SCAD penalty is proposed. It can simultaneously select significant variables in the parametric and nonparametric components and estimate the nonzero regression coefficients and coefficient functions. The consistency of the variable selection procedure and the oracle property of the penalized least-squares estimators for high-dimensional data are established. Some simulations and the real data analysis are constructed to illustrate the finite sample performances of the proposed method.

翻译：本文聚焦于部分线性单指标变系数模型的变量选择问题。提出了一种结合基函数逼近与SCAD惩罚的正则化变量选择方法。该方法能够同时筛选参数分量与非参数分量中的显著变量，并估计非零回归系数及系数函数。本文建立了变量选择过程的一致性，并证明了高维数据下惩罚最小二乘估计量的oracle性质。通过数值模拟与实证数据分析，验证了所提方法在有限样本下的表现。