Optimization study of high-dimensional varying coefficient partially linear model based on elastic network

Abstract

In this paper, we study the high-dimensional varying coefficient partially linear model and proposes a variable parameter selection method combined with elastic network. The two-stage estimation method is adopted and the alternating direction multiplier method (ADMM) is used to solve the model. Firstly, based on the varying coefficient partially linear model, we use local polynomial estimation method to estimate the non-parametric part of the model and convert it into a parametric model. Secondly, the elastic network regularization term is introduced into the model for variable selection, and the alternating direction multiplier method (ADMM) is used to solve the model. Then, the convergence of the algorithm is proved under certain conditions. Finally, the proposed method has been validated to have good effectiveness and certain practicality through numerical simulation of two types of high-dimensional datasets and example analysis.