A simple tuning parameter selection method for high dimensional regression

The penalized regression is an important technique for high-dimensional data analysis, but penalized estimation method hinge on finding a suitable choice of tuning parameter. In this paper, a simple modified L curve method is proposed to select the tuning parameter for penalized estimation including Lasso, SCAD and MCP in linear regression models. Through data simulation and actual data analysis, we find that the modified L curve method can be simpler and more accurate than traditional tuning parameter selection schemes such as CV and BIC. Furthermore, the method is able to identify the true model consistently and has the less model error, especially for the cases where there is a high correlation between predictors.