A New Ridge-Type Estimator for the Linear Regression Model: Simulations and Applications

Table 2

Estimated MSE when n = 30, , and ρ = 0.90 and 0.99.

n = 30	0.9					0.99
Sigma	k = d	OLS	Ridge	Liu	New est	OLS	Ridge	Liu	New est
1	0.1	1.154	1.012	0.532	0.883	12.774	4.155	0.857	1.128
	0.2		0.899	0.583	0.691		2.339	1.388	1.946
	0.3		0.809	0.638	0.555		1.603	2.117	3.278
	0.4		0.736	0.697	0.459		1.214	3.045	4.416
	0.5		0.675	0.762	0.392		0.978	4.170	5.340
	0.6		0.625	0.831	0.346		0.821	5.495	6.097
	0.7		0.582	0.905	0.317		0.712	7.017	6.725
	0.8		0.545	0.983	0.299		0.631	8.738	7.255
	0.9		0.514	1.066	0.291		0.571	10.656	7.708
	1		0.487	1.154	0.289		0.524	12.774	8.100
5	0.1	28.461	24.840	12.067	21.501	319.335	102.389	17.451	23.383
	0.2		21.945	13.492	16.402		56.008	31.445	40.368
	0.3		19.588	15.017	12.625		36.978	50.327	71.447
	0.4		17.641	16.640	9.805		26.816	74.095	98.322
	0.5		16.010	18.362	7.690		20.580	102.751	120.269
	0.6		14.627	20.184	6.104		16.415	136.293	138.268
	0.7		13.442	22.105	4.917		13.467	174.723	153.240
	0.8		12.418	24.124	4.036		11.293	218.040	165.880
	0.9		11.526	26.243	3.393		9.637	266.244	176.695
	1		10.741	28.461	2.935		8.343	319.335	186.058
10	0.1	113.841	99.331	48.088	85.947	1277.429	409.249	69.149	92.868
	0.2		87.726	53.814	65.494		223.571	125.195	160.554
	0.3		78.277	59.935	50.326		147.369	200.793	284.749
	0.4		70.466	66.450	38.986		106.666	295.943	392.184
	0.5		63.919	73.361	30.469		81.687	410.644	479.940
	0.6		58.368	80.667	24.064		64.998	544.898	551.916
	0.7		53.612	88.368	19.262		53.189	698.703	611.794
	0.8		49.498	96.464	15.687		44.476	872.060	662.350
	0.9		45.910	104.955	13.064		37.839	1064.960	705.611
	1		42.758	113.841	11.182		32.655	1277.429	743.065