基于ArctanLASSO的參數估計和變量選取

Motivated by SICA（smooth integration of counting and absolute deviation） method, this paper proposes a class of concave penalties called Arctan LASSO（Arctangent least absolute shrinkage and selection operator） based on arctangent function. The Arctan LASSO is an alternative smoothing method from L0 to L1 penalty which can be used for simultaneous variable selection and coefficient estimation. The n1/2consistency and oracle property are proved for the Arctan LASSO estimator. An efficient iterate algorithm by LLA（locallinear approximation） and coordination descent method is proposed with tuning parameter chosen via the BIC（Bayesian information criterion） criterion. Simulation analysis shows that Arctan LASSO 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