Heterogeneous robust estimation with the mixed penalty in high-dimensional regression model

In this paper, we propose a MIXED penalty for the LAD regression model, which can estimate parameters and select important variables efficiently and stably. The proposed method has a good performance in the case of dependent variable with heavy tail and outliers, so this estimator is robust and efficient for tackling the problem of heterogeniety. We show that the proposed estimator possesses the good properties by applying certain assumptions. In the part of numerical simulation, we give several simulation studies to examine the asymptotic results, which shows that the method we proposed behaves better.