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

Table 1

Estimated MSE when n = 30, , and ρ = 0.70 and 0.80.

n = 30	0.7					0.8
Sigma	k = d	OLS	Ridge	Liu	New est	OLS	Ridge	Liu	New est
1	0.1	0.362	0.352	0.291	0.342	0.547	0.519	0.375	0.491
	0.2		0.342	0.298	0.323		0.493	0.391	0.444
	0.3		0.333	0.305	0.307		0.470	0.407	0.404
	0.4		0.325	0.312	0.293		0.449	0.425	0.370
	0.5		0.317	0.320	0.280		0.431	0.443	0.342
	0.6		0.309	0.328	0.268		0.414	0.462	0.318
	0.7		0.302	0.336	0.258		0.398	0.482	0.299
	0.8		0.296	0.344	0.249		0.384	0.503	0.282
	0.9		0.290	0.353	0.242		0.372	0.525	0.269
	1.0		0.284	0.362	0.235		0.360	0.547	0.258
5	0.1	8.021	7.759	6.137	7.501	12.967	12.232	8.364	11.522
	0.2		7.511	6.331	7.021		11.567	8.817	10.261
	0.3		7.277	6.529	6.577		10.962	9.284	9.156
	0.4		7.056	6.731	6.165		10.411	9.766	8.186
	0.5		6.846	6.937	5.784		9.907	10.263	7.333
	0.6		6.647	7.146	5.430		9.445	10.775	6.581
	0.7		6.459	7.359	5.102		9.019	11.301	5.918
	0.8		6.280	7.576	4.797		8.626	11.842	5.331
	0.9		6.109	7.797	4.513		8.263	12.397	4.813
	1.0		5.947	8.021	4.250		7.926	12.967	4.354
10	0.1	31.993	30.939	24.421	29.907	51.819	48.871	33.333	46.022
	0.2		29.945	25.203	27.977		46.201	35.155	40.955
	0.3		29.005	26.000	26.189		43.775	37.034	36.514
	0.4		28.116	26.812	24.532		41.561	38.972	32.612
	0.5		27.274	27.639	22.995		39.536	40.968	29.176
	0.6		26.474	28.480	21.568		37.677	43.022	26.145
	0.7		25.715	29.336	20.241		35.966	45.134	23.466
	0.8		24.994	30.207	19.008		34.387	47.304	21.096
	0.9		24.307	31.092	17.860		32.926	49.532	18.996
	1.0		23.654	31.993	16.791		31.570	51.819	17.134