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

Table 4

Estimated MSE when n = 100, , 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	0.287	0.278	0.230	0.270	3.072	2.141	0.688	1.423
	0.2		0.270	0.236	0.255		1.621	0.836	0.769
	0.3		0.263	0.241	0.242		1.298	1.013	0.528
	0.4		0.256	0.247	0.231		1.083	1.219	0.472
	0.5		0.250	0.253	0.221		0.930	1.455	0.506
	0.6		0.244	0.259	0.213		0.819	1.720	0.583
	0.7		0.239	0.265	0.206		0.733	2.014	0.680
	0.8		0.234	0.272	0.200		0.667	2.337	0.785
	0.9		0.230	0.279	0.195		0.613	2.690	0.892
	1		0.226	0.287	0.191		0.570	3.072	0.997
5	0.1	6.958	6.719	5.256	6.486	76.772	53.314	14.746	34.689
	0.2		6.495	5.431	6.050		39.905	18.971	16.660
	0.3		6.283	5.610	5.649		31.412	23.862	8.834
	0.4		6.083	5.792	5.278		25.626	29.420	5.803
	0.5		5.893	5.977	4.935		21.466	35.645	5.174
	0.6		5.714	6.166	4.617		18.350	42.537	5.795
	0.7		5.544	6.359	4.324		15.939	50.096	7.072
	0.8		5.383	6.555	4.052		14.024	58.321	8.686
	0.9		5.230	6.754	3.799		12.471	67.213	10.458
	1		5.085	6.958	3.566		11.189	76.772	12.287
10	0.1	27.809	26.853	20.970	25.916	307.086	213.255	58.717	138.685
	0.2		25.951	21.675	24.167		159.582	75.683	66.354
	0.3		25.100	22.394	22.551		125.559	95.308	34.815
	0.4		24.296	23.126	21.056		102.365	117.590	22.463
	0.5		23.535	23.872	19.672		85.681	142.529	19.743
	0.6		22.815	24.632	18.389		73.175	170.126	22.045
	0.7		22.131	25.406	17.200		63.493	200.380	26.995
	0.8		21.482	26.193	16.096		55.802	233.291	33.308
	0.9		20.865	26.994	15.071		49.561	268.860	40.270
	1		20.279	27.809	14.120		44.407	307.086	47.470