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

Table 6

Estimated MSE when n = 30, , and ρ = 0.9 and 0.99.

N = 30	0.9					0.99
Sigma	k = d	OLS	Ridge	Liu	New ridge	OLS	Ridge	Liu	New ridge
1	0.1	2.52	2.27	1.29	2.03	28.68	11.20	2.26	4.45
	0.2		2.06	1.39	1.66		6.82	3.55	4.16
	0.3		1.88	1.51	1.37		4.78	5.25	5.78
	0.4		1.73	1.63	1.16		3.62	7.36	7.58
	0.5		1.61	1.76	0.99		2.88	9.89	9.25
	0.6		1.50	1.90	0.85		2.37	12.83	10.75
	0.7		1.41	2.04	0.75		2.01	16.17	12.07
	0.8		1.32	2.20	0.68		1.74	19.93	13.24
	0.9		1.25	2.35	0.62		1.54	24.10	14.27
	1		1.18	2.52	0.57		1.38	28.68	15.19
5	0.1	63.03	56.58	31.23	50.57	717.09	278.85	50.83	108.00
	0.2		51.27	34.11	41.03		168.23	84.11	97.17
	0.3		46.82	37.15	33.61		116.38	127.57	134.54
	0.4		43.03	40.35	27.78		86.52	181.23	176.89
	0.5		39.77	43.72	23.14		67.36	245.07	216.47
	0.6		36.94	47.25	19.42		54.18	319.10	251.87
	0.7		34.45	50.95	16.43		44.67	403.32	283.16
	0.8		32.25	54.81	14.01		37.54	497.72	310.80
	0.9		30.28	58.84	12.06		32.06	602.31	335.29
	1		28.52	63.03	10.48		27.73	717.09	357.10
10	0.1	252.14	226.30	124.75	202.23	2868.35	1115.06	202.39	431.48
	0.2		205.03	136.28	164.03		672.43	335.62	387.84
	0.3		187.21	148.46	134.32		464.91	509.59	537.07
	0.4		172.05	161.30	110.91		345.38	724.31	706.26
	0.5		158.99	174.79	92.29		268.65	979.78	864.43
	0.6		147.63	188.95	77.37		215.88	1276.00	1005.86
	0.7		137.66	203.76	65.34		177.77	1612.96	1130.89
	0.8		128.82	219.23	55.62		149.24	1990.68	1241.34
	0.9		120.95	235.35	47.75		127.25	2409.14	1339.21
	1		113.89	252.14	41.38		109.92	2868.35	1426.34