Abstract: Based on the general linear regression model, this paper considers the heterogeneity of individual intercepts and the high dimensional covariates in the model. In order to deal with the problem of data anomalies and improve the robustness of the model, we adopt Huber loss function. Meanwhile, we propose a center-based penalty to identify potential subgroups and implement covariates selection by using concave penalty. In the aspect of algorithm, we design a new hybrid algorithm based on alternating direction multiplier method (ADMM) and coordinate descent method to solve the objective function. At the theoretical level, this paper successfully constructs the asymptotic property of Oracle estimators, and rigorously proves its close relationship with the objective function, which guarantees the effectiveness of the proposed method in potential subgroup identification and variable selection. Numerical simulation and empirical data analysis fully demonstrate the robustness and effectiveness of the proposed method in subgroup identification and high-dimensional data processing.

Key words: Huber loss, subgroup analysis, high-dimensional data, Oracle properties