Hui Qi, Yuanshan Wu, Mingqiu Wang, Jiayu Huang
The least square Lasso estimator for high-dimensional sparse linear model may arise several limitations in practical applications due to the dependence of the tuning parameter on the variance of model error. The square root Lasso estimator is proposed to make the tuning parameter free of the variance of the model error, which however exhibits some weakness from the perspective of robustness. Furthermore, the least absolute deviation Lasso estimator achieves some robustness, but it requires that the density of model error is bounded away from zero at some specific point. We propose a novel pairwise square root Lasso estimator for high-dimensional sparse linear model which only assumes that distribution of the model error is symmetric. The proposed estimator enjoys the advantage of tuning-free parameter and enables to address much heavier tailed model errors than the least absolute deviation Lasso estimator. We establish the error bound and consistency of variable selection for pairwise square root Lasso approach. Simulation studies demonstrate some favorable and compelling performances of the proposed method in some typical scenarios. A real example is analyzed to show the practical effectiveness of the proposed method.
