Variable Selection and Parameter Estimation with the Atan Regularization Method

Table 3

Simulation results for linear regression models of Example 9.

Method	MRME	Number of zeros		Proportion of
		C	IC	Underfit	Correct-fit	Overfit
,
Lasso	0.9955	4.9900	2.0100	0.0100	0.1150	0.8750
Alasso	0.5740	4.8650	0.1100	0.1350	0.8150	0.0500
SCAD	0.5659	4.9800	0.5600	0.0200	0.5600	0.4200
MCP	0.6177	4.9100	0.1200	0.0900	0.8250	0.0850
Dantzig	0.6987	4.8900	0.6700	0.1100	0.4360	0.4540
Bayesian	0.5656	4.8650	0.2500	0.1350	0.6340	0.2310
Atan	0.5447	4.8900	0.1150	0.1100	0.8250	0.0650
,
Lasso	1.2197	5.0000	2.0650	0.0000	0.1400	0.8600
Alasso	0.4458	4.9950	0.0900	0.0050	0.9250	0.0700
SCAD	0.4481	5.0000	0.4850	0.0000	0.6350	0.3650
MCP	0.4828	5.0000	0.1150	0.0000	0.8950	0.1050
Dantzig	0.7879	5.0000	0.5670	0.0000	0.3200	0.6800
Bayesian	0.4237	5.0000	0.1800	0.0000	0.7550	0.2450
Atan	0.4125	4.9950	0.0250	0.0050	0.9700	0.0250
,
Lasso	1.2004	5.0000	2.5700	0.0000	0.0900	0.9100
Alasso	0.3156	5.0000	0.0700	0.0000	0.9300	0.0700
SCAD	0.3219	5.0000	0.6550	0.0000	0.5950	0.4050
MCP	0.3220	5.0000	0.0750	0.0000	0.9300	0.0700
Dantzig	0.5791	5.0000	0.5470	0.0000	0.3400	0.6600
Bayesian	0.3275	5.0000	0.2800	0.0000	0.6750	0.3250
Atan	0.3239	5.0000	0.0750	0.0000	0.9350	0.0650