The Study About SCAD Based On Simulation

In this paper, we employ numerical simulations to study the problems in the pro-cedure of variable selection using SCAD. Three points in SCAD are studied using sim-ulations. Firstly, Fan and Li (2001) had proposed three mathematical conditions that a good penalty function should have. Here, we study one condition, sparsity, and obtain a new nonconcave penalty function which is smoother than the SCAD. These two penalty functions are compared based on numerical simulations and the results are satisfied. Note that the tuning parameter in the method of penalized likelihood is important, we study the effect of the two kinds of threshold on the tuning parameter employing simulations under two criterions, BIC and GCV, respectively. What's more, we obtain intuitive evidence of that BIC can reduce the possibility of over-fitting that GCV shares, which is useful for the practitioner. Besides, two styles of approximation method in the procedure of SCAD are studied in this paper. The performance in variable selection is shown using simulations.