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

Table 1

Variable selections for and under different and different when .

	Method
		GMSE	C	I	GMSE	C	I	GMSE	C	I
(0, 5, 50)	AdLasso	0.0662	2.934	0	0.0307	2.982	0	0.0156	2.996	0
	SCAD	0.0678	2.730	0	0.0356	2.752	0	0.0198	2.830	0
	Oracle	0.0621	3.000	0	0.0299	3.000	0	0.0151	3.000	0
(0, 10, 100)	AdLasso	0.0367	7.986	0	0.0170	7.996	0	0.0082	8.000	0
	SCAD	0.0341	7.988	0	0.0176	7.990	0	0.0082	7.990	0
	Oracle	0.0292	8.000	0	0.0153	8.000	0	0.0075	8.000	0
(0, 15, 150)	AdLasso	0.0220	12.946	0	0.0101	12.976	0	0.0053	12.976	0
	SCAD	0.0224	12.972	0	0.0119	12.982	0	0.0069	12.984	0
	Oracle	0.0192	13.000	0	0.0100	13.000	0	0.0050	13.000	0
(0.3, 5, 50)	AdLasso	0.1102	1.910	0	0.0507	1.990	0	0.0233	1.994	0
	SCAD	0.0795	1.938	0	0.0485	1.964	0	0.0236	1.964	0
	Oracle	0.0765	2.000	0	0.0413	2.000	0	0.0194	2.000	0
(0.3, 10, 100)	AdLasso	0.0584	6.942	0	0.0244	6.978	0	0.0114	7.000	0
	SCAD	0.0435	6.970	0	0.0204	6.976	0	0.0125	6.986	0
	Oracle	0.0383	7.000	0	0.0201	7.000	0	0.0097	7.000	0
(0.3, 15, 150)	AdLasso	0.0327	11.934	0	0.0156	11.992	0	0.0075	12.000	0
	SCAD	0.0291	11.998	0	0.0174	11.998	0	0.0075	11.998	0
	Oracle	0.0259	12.000	0	0.0128	12.000	0	0.0069	12.000	0
(0.5, 5, 50)	AdLasso	0.0908	1.978	0	0.0486	1.998	0	0.0221	2.000	0
	SCAD	0.0779	1.950	0	0.0447	1.974	0	0.0233	1.988	0
	Oracle	0.0764	2.000	0	0.0388	2.000	0	0.0206	2.000	0
(0.5, 10, 100)	AdLasso	0.0436	6.970	0	0.0210	7.000	0	0.0108	7.000	0
	SCAD	0.0417	6.980	0	0.0201	6.980	0	0.0106	6.996	0
	Oracle	0.0381	7.000	0	0.0199	7.000	0	0.0091	7.000	0
(0.5, 15, 150)	AdLasso	0.0289	11.990	0	0.0146	11.998	0	0.0070	11.998	0
	SCAD	0.0268	11.998	0	0.0145	11.998	0	0.0074	12.000	0
	Oracle	0.0262	12.000	0	0.0129	12.000	0	0.0066	12.000	0
(0.7, 5, 50)	AdLasso	0.0967	1.984	0	0.0442	1.998	0	0.0206	2.000	0
	SCAD	0.0844	1.945	0	0.0453	1.992	0	0.0226	1.994	0
	Oracle	0.0827	2.000	0	0.0402	2.000	0	0.0192	2.000	0
(0.7, 10, 100)	AdLasso	0.0467	6.996	0	0.0199	7.000	0	0.0096	7.000	0
	SCAD	0.0446	6.998	0	0.0210	7.000	0	0.0098	7.000	0
	Oracle	0.0395	7.000	0	0.0191	7.000	0	0.0094	7.000	0
(0.7, 15, 150)	AdLasso	0.0265	11.980	0	0.0138	11.998	0	0.0070	12.000	0
	SCAD	0.0259	11.996	0	0.0136	12.000	0	0.0074	12.000	0
	Oracle	0.0255	12.000	0	0.0126	12.000	0	0.0065	12.000	0