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

Table 8

Estimated MSE when n = 100, , and ρ = 0.90 and 0.99.

n = 100	0.9					0.99
Sigma	k = d	OLS	Ridge	Liu	New ridge	OLS	Ridge	Liu	New ridge
1	0.1	0.546	0.529	0.431	0.512	6.389	4.391	1.624	2.949
	0.2		0.513	0.442	0.482		3.407	1.934	1.836
	0.3		0.498	0.454	0.456		2.819	2.298	1.453
	0.4		0.485	0.466	0.432		2.423	2.718	1.347
	0.5		0.472	0.478	0.411		2.135	3.192	1.359
	0.6		0.460	0.491	0.392		1.914	3.721	1.426
	0.7		0.449	0.504	0.375		1.738	4.306	1.519
	0.8		0.439	0.517	0.360		1.593	4.945	1.625
	0.9		0.429	0.531	0.346		1.472	5.640	1.737
	1		0.420	0.546	0.334		1.370	6.389	1.851
5	0.1	13.640	13.216	10.676	12.802	159.732	109.722	38.895	73.284
	0.2		12.820	10.979	12.037		84.915	47.018	44.506
	0.3		12.448	11.289	11.336		69.971	56.467	33.865
	0.4		12.099	11.605	10.693		59.823	67.242	30.146
	0.5		11.770	11.928	10.102		52.370	79.343	29.417
	0.6		11.460	12.257	9.558		46.597	92.769	30.090
	0.7		11.168	12.593	9.056		41.953	107.521	31.455
	0.8		10.891	12.935	8.593		38.114	123.599	33.171
	0.9		10.628	13.284	8.165		34.875	141.003	35.063
	1		10.379	13.640	7.768		32.097	159.732	37.036
10	0.1	54.558	52.866	42.699	51.212	638.928	438.910	155.399	293.121
	0.2		51.282	43.914	48.150		339.663	187.945	177.874
	0.3		49.796	45.155	45.344		279.860	225.785	135.151
	0.4		48.399	46.422	42.768		239.236	268.921	120.120
	0.5		47.084	47.714	40.397		209.391	317.351	117.053
	0.6		45.843	49.032	38.214		186.265	371.077	119.599
	0.7		44.670	50.375	36.198		167.659	430.097	124.922
	0.8		43.560	51.744	34.336		152.274	494.412	131.654
	0.9		42.508	53.138	32.612		139.287	564.022	139.094
	1		41.509	54.558	31.014		128.149	638.928	146.866