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

Table 2

Variable selections for and under different and different when .

	Method
		GMSE	C	I	GMSE	C	I	GMSE	C	I
(0, 5, 50)	AdLasso	0.0708	2.932	0	0.0318	2.976	0	0.0162	2.996	0
	SCAD	0.0742	2.690	0.006	0.0404	2.740	0.002	0.0233	2.810	0
	Oracle	0.0641	3.000	0	0.0299	3.000	0	0.0153	3.000	0
(0, 10, 100)	AdLasso	0.0369	7.974	0.002	0.0172	7.984	0	0.0090	7.986	0
	SCAD	0.0405	7.980	0.002	0.0168	7.980	0.002	0.0089	7.982	0
	Oracle	0.0297	8.000	0	0.0159	8.000	0	0.0080	8.000	0
(0, 15, 150)	AdLasso	0.0246	12.936	0.002	0.0121	12.974	0	0.0055	12.976	0
	SCAD	0.0272	12.968	0	0.0146	12.976	0	0.0073	12.980	0
	Oracle	0.0220	13.000	0	0.0102	13.000	0	0.0055	13.000	0
(0.3, 5, 50)	AdLasso	0.1230	1.910	0.002	0.0538	1.972	0.002	0.0234	1.992	0
	SCAD	0.1033	1.914	0	0.0561	1.952	0	0.0237	1.952	0
	Oracle	0.0768	2.000	0	0.0472	2.000	0	0.0205	2.000	0
(0.3, 10, 100)	AdLasso	0.0584	6.942	0	0.0288	6.978	0	0.0120	6.998	0
	SCAD	0.0460	6.956	0.002	0.0263	6.964	0	0.0136	6.982	0
	Oracle	0.0440	7.000	0	0.0205	7.000	0	0.0110	7.000	0
(0.3, 15, 150)	AdLasso	0.0403	11.934	0	0.0167	11.984	0	0.0075	11.998	0
	SCAD	0.0384	11.992	0	0.0201	11.992	0	0.0101	11.994	0
	Oracle	0.0272	12.000	0	0.0132	12.000	0	0.0069	12.000	0
(0.5, 5, 50)	AdLasso	0.1016	1.968	0.006	0.0514	1.998	0.002	0.0224	2.000	0
	SCAD	0.0961	1.938	0.002	0.0470	1.972	0.002	0.0254	1.980	0
	Oracle	0.0790	2.000	0	0.0394	2.000	0	0.0216	2.000	0
(0.5, 10, 100)	AdLasso	0.0466	6.968	0	0.0226	6.998	0	0.0116	7.000	0
	SCAD	0.0456	6.964	0	0.0236	6.972	0	0.0123	6.994	0
	Oracle	0.0389	7.000	0	0.0129	7.000	0	0.0098	7.000	0
(0.5, 15, 150)	AdLasso	0.0285	11.986	0	0.0158	11.992	0	0.0078	11.998	0
	SCAD	0.0278	11.996	0	0.0161	11.998	0	0.0089	12.000	0
	Oracle	0.0277	12.000	0	0.0132	12.000	0	0.0069	12.000	0
(0.7, 5, 50)	AdLasso	0.0984	1.970	0.004	0.0447	1.998	0	0.0214	2.000	0
	SCAD	0.0971	1.940	0.002	0.0463	1.982	0	0.0236	1.988	0
	Oracle	0.0827	2.000	0	0.0405	2.000	0	0.0210	2.000	0
(0.7, 10, 100)	AdLasso	0.0515	6.974	0	0.0346	6.988	0	0.0096	7.000	0
	SCAD	0.0530	6.992	0	0.0275	6.994	0	0.0100	6.998	0
	Oracle	0.0398	7.000	0	0.0195	7.000	0	0.0095	7.000	0
(0.7, 15, 150)	AdLasso	0.0291	11.980	0	0.0142	11.996	0	0.0082	12.000	0
	SCAD	0.0318	11.994	0	0.0157	12.000	0	0.0091	12.000	0
	Oracle	0.0273	12.000	0	0.0127	12.000	0	0.0068	12.000	0