Variable Selection of High-Dimensional Spatial Autoregressive Panel Models with Fixed Effects

Table 3

Variable selections for and under different and different when .

	Method
		GMSE	C	I	GMSE	C	I	GMSE	C	I
(0, 7, 6)	AdLasso	0.0273	4.988	0	0.0125	4.990	0	0.0061	4.994	0
	SCAD	0.0265	4.992	0	0.0123	4.992	0	0.0061	5.000	0
	Oracle	0.0239	5.000	0	0.0116	5.000	0	0.0061	5.000	0
(0, 8, 9)	AdLasso	0.0143	5.970	0	0.0072	5.976	0	0.0037	6.000	0
	SCAD	0.0153	5.970	0	0.0072	5.970	0	0.0037	6.000	0
	Oracle	0.0140	6.000	0	0.0070	6.000	0	0.0037	6.000	0
(0, 9, 12)	AdLasso	0.0111	6.978	0	0.0055	7.000	0	0.0027	7.000	0
	SCAD	0.0116	6.976	0	0.0055	7.000	0	0.0028	7.000	0
	Oracle	0.0108	7.000	0	0.0051	7.000	0	0.0027	7.000	0
(0.3, 7, 6)	AdLasso	0.0350	3.938	0	0.0173	3.994	0	0.0082	3.996	0
	SCAD	0.0350	3.950	0	0.0166	3.994	0	0.0081	4.000	0
	Oracle	0.0308	4.000	0	0.0162	4.000	0	0.0079	4.000	0
(0.3, 8, 9)	AdLasso	0.0213	4.970	0	0.0099	4.988	0	0.0052	5.000	0
	SCAD	0.0206	4.974	0	0.0096	4.990	0	0.0055	4.992	0
	Oracle	0.0204	5.000	0	0.0096	5.000	0	0.0051	5.000	0
(0.3, 9, 12)	AdLasso	0.0158	5.986	0	0.0079	6.000	0	0.0046	6.000	0
	SCAD	0.0152	5.984	0	0.0079	6.000	0	0.0046	6.000	0
	Oracle	0.0143	6.000	0	0.0077	6.000	0	0.0038	6.000	0
(0.5, 7, 6)	AdLasso	0.0329	3.958	0	0.0163	3.994	0	0.0081	3.996	0
	SCAD	0.0345	3.970	0	0.0165	3.996	0	0.0081	3.998	0
	Oracle	0.0326	4.000	0	0.0159	4.000	0	0.0080	4.000	0
(0.5, 8, 9)	AdLasso	0.0192	4.970	0	0.0095	4.998	0	0.0048	5.000	0
	SCAD	0.0201	4.990	0	0.0098	4.998	0	0.0057	5.000	0
	Oracle	0.0185	5.000	0	0.0090	5.000	0	0.0046	5.000	0
(0.5, 9, 12)	AdLasso	0.0147	5.988	0	0.0072	6.000	0	0.0039	6.000	0
	SCAD	0.0152	5.992	0	0.0074	6.000	0	0.0040	6.000	0
	Oracle	0.0139	6.000	0	0.0069	6.000	0	0.0037	6.000	0
(0.7, 7, 6)	AdLasso	0.0331	3.974	0	0.0164	3.996	0	0.0082	4.000	0
	SCAD	0.0353	3.984	0	0.0167	3.998	0	0.0081	4.000	0
	Oracle	0.0326	4.000	0	0.0156	4.000	0	0.0079	4.000	0
(0.7, 8, 9)	AdLasso	0.0193	4.964	0	0.0095	4.998	0	0.0048	5.000	0
	SCAD	0.0212	4.984	0	0.0099	4.998	0	0.0052	5.000	0
	Oracle	0.0191	5.000	0	0.0093	5.000	0	0.0046	5.000	0
(0.7, 9, 12)	AdLasso	0.0148	5.994	0	0.0072	6.000	0	0.0038	6.000	0
	SCAD	0.0162	6.000	0	0.0077	6.000	0	0.0040	6.000	0
	Oracle	0.0144	6.000	0	0.0071	6.000	0	0.0038	6.000	0