Research Based on High-Dimensional Fused Lasso Partially Linear Model

In this paper, a partially linear model based on the fused lasso method is proposed to solve the problem of high correlation between adjacent variables, and then the idea of the two-stage estimation method is used to study the solution of this model. Firstly, the non-parametric part of the partially linear model is estimated using the kernel function method and transforming the semiparametric model into a parametric model. Secondly, the fused lasso regularization term is introduced into the model to construct the least squares parameter estimation based on the fused lasso penalty. Then, due to the non-smooth terms of the model, the subproblems may not have closed-form solutions, so the linearized alternating direction multiplier method (LADMM) is used to solve the model, and the convergence of the algorithm and the asymptotic properties of the model are analyzed. Finally, the applicability of this model was demonstrated through two types of simulation data and practical problems in predicting worker wages.