Application of the ADMM Algorithm for a High-Dimensional Partially Linear Model

This paper focuses on a high-dimensional semi-parametric regression model in which a partially linear model is used for the parametric part and the B-spline basis function approach is used to estimate the unknown function for the non-parametric part. Within the framework of this model, the constrained least squares estimation is investigated, and the alternating-direction multiplier method (ADMM) is used to solve the model. The convergence is proved under certain conditions. Finally, numerical simulations are performed and applied to workers’ wage data from CPS85. The results show that the ADMM algorithm is very effective in solving high-dimensional partially linear models.