部分线性可加模型的两步SCAD惩罚估计与模型识别

Partly Linear Additive Model (PLAM) has attracted wide attention because it is more extensive. It has greater flexibility than linear model. It can fit high-dimensional data when completely nonparametric model becomes unworkable. We consider the problem of using spline approximation and two-step SCAD penalty to assist variable selection and parameter component identification. Considering the estimation and variable selection process of PLAM based on weighted compound quantile regression (WCQR), the advantage of our method is that the linear zero component can be quickly identified, and then the parametric part and the non-parametric part can be distinguished from the remaining covariables. Under mild conditions, we prove the theoretical properties of the estimator obtained. In addition, the proposed method can recognize the true model when the probability is close to 1.