High-dimensional penalized quantile regression and optimization algorithm

For linear regression models of high-dimensional data with outliers, a new penalized quantile estimation was proposed based on error function regularization．Compared with classical penalized method, the proposed method had stronger robustness and smaller estimation bias and prediction errors．To solve computational challenges caused by non-smoothness of quantile loss function and non-convexity of error function, an efficient IRW-ADMM algorithm was proposed to obtain numerical solutions of regression coefficients by combining iterative reweighted algorithm and ADMM algorithm．Simulations showed that the proposed method has better performance in terms of parameter estimation and variable selection compared with existing penalized quantile estimators．This method was further applied to riboflavin gene data analysis to confirm its validity and feasibility．