Parameter estimation and variable selection via ArctanLASSO

Abstract

Motivated by SICA (smooth integration of counting and absolute deviation) method, this paper proposes a class of concave penalties called ArctanLASSO (Arctangent least absolute shrinkage and selection operator) based on arctangent function. The ArctanLASSO is an alternative smoothing method from $L_0$ to $L_1$ penalty which can be used for simultaneous variable selection and coefficient estimation. The $n^{1/2}$ consistency and oracle property are proved for the ArctanLASSO estimator. An efficient iterate algorithm by LLA (local linear approximation) and coordination descent method is proposed with tuning parameter chosen via the BIC (Bayesian information criterion) criterion. Simulation analysis shows that ArctanLASSO estimator is similar to SICA, and has comparable performance in estimate accuracy and better performance in variable selection than LASSO, SCAD (smoothly clipped absolute deviation), MCP (minimax concave penalty) and adaptive LASSO. The method is meaningful for selecting the significant variables in the empirical analysis.