Modified One-Parameter Liu Estimator for the Linear Regression Model

Table 6

Estimated MSE when and .

		0.7				0.8				0.9				0.99
		OLS	Ridge	Liu	MLiu	OLS	Ridge	Liu	MLiu	OLS	Ridge	Liu	MLiu	OLS	Ridge	Liu	MLiu
1	0.1	0.2225	0.2195	0.1989	0.1942	0.3446	0.3366	0.2865	0.2751	0.7153	0.6783	0.4938	0.4543	7.4001	4.6647	1.6335	1.1431
	0.2	0.2225	0.2165	0.2014	0.1919	0.3446	0.3290	0.2924	0.2697	0.7153	0.6453	0.5149	0.4358	7.4001	3.4961	1.9866	1.0057
	0.3	0.2225	0.2137	0.2038	0.1896	0.3446	0.3218	0.2985	0.2643	0.7153	0.6158	0.5369	0.4182	7.4001	2.8469	2.4116	0.9403
	0.4	0.2225	0.2110	0.2064	0.1874	0.3446	0.3150	0.3046	0.2591	0.7153	0.5892	0.5597	0.4015	7.4001	2.4268	2.9085	0.9468
	0.5	0.2225	0.2084	0.2090	0.1852	0.3446	0.3085	0.3110	0.2540	0.7153	0.5652	0.5835	0.3857	7.4001	2.1278	3.4773	1.0252
	0.6	0.2225	0.2058	0.2116	0.1831	0.3446	0.3024	0.3174	0.2491	0.7153	0.5434	0.6081	0.3707	7.4001	1.9014	4.118	1.1755
	0.7	0.2225	0.2034	0.2142	0.1810	0.3446	0.2966	0.3240	0.2443	0.7153	0.5236	0.6336	0.3566	7.4001	1.7224	4.8307	1.3977
	0.8	0.2225	0.2010	0.2169	0.1789	0.3446	0.2910	0.3308	0.2397	0.7153	0.5055	0.6599	0.3434	7.4001	1.5767	5.6152	1.6918
	0.9	0.2225	0.1987	0.2197	0.1769	0.3446	0.2858	0.3376	0.2352	0.7153	0.4889	0.6872	0.3311	7.4001	1.4552	6.4717	2.0578
	1.0	0.2225	0.1965	0.2225	0.1750	0.3446	0.2808	0.3446	0.2308	0.7153	0.4736	0.7153	0.3197	7.4001	1.3523	7.4001	2.4958
5	0.1	5.5620	5.4869	4.9618	4.8354	8.6161	8.4163	7.1380	6.8372	17.882	16.960	12.260	11.220	185.00	116.57	39.235	26.109
	0.2	5.5620	5.4139	5.0260	4.7731	8.6161	8.2263	7.2921	6.6906	17.882	16.134	12.809	10.728	185.00	87.159	48.425	22.173
	0.3	5.5620	5.3430	5.0908	4.7115	8.6161	8.0453	7.4488	6.5466	17.882	15.390	13.377	10.256	185.00	70.707	59.367	19.988
	0.4	5.5620	5.2741	5.1562	4.6505	8.6161	7.8728	7.6980	6.4050	17.882	14.717	13.963	9.8020	185.00	59.977	72.060	19.556
	0.5	5.5620	5.2071	5.2223	4.5901	8.6161	7.7081	7.7697	6.2660	17.882	14.105	15.687	9.3674	185.00	52.275	86.505	20.874
	0.6	5.5620	5.1419	5.2890	4.5304	8.6161	7.5508	7.9339	6.1294	17.882	13.546	15.193	8.9517	185.00	46.388	102.70	23.944
	0.7	5.5620	5.0785	5.3563	4.4712	8.6161	7.4004	8.1007	5.9954	17.882	13.035	16.000	8.5551	185.00	41.691	120.65	28.766
	0.8	5.5620	5.0169	5.4242	4.4128	8.6161	7.2565	8.2700	5.8640	17.882	12.565	16.500	8.1774	185.00	37.827	140.35	35.339
	0.9	5.5620	4.9568	5.4928	4.3549	8.6161	7.1186	8.4418	5.7350	17.882	12.131	17.181	7.8188	185.00	34.577	161.80	43.664
	1.0	5.5620	4.8983	5.5620	4.2977	8.6161	6.9863	8.6161	5.6086	17.882	11.731	17.882	7.4791	185.00	31.796	185.00	53.740
10	0.1	22.248	21.948	19.849	19.343	34.464	33.666	28.553	27.349	71.528	67.843	49.040	44.873	740.01	466.29	156.77	104.14
	0.2	22.248	21.656	20.106	19.093	34.464	32.907	29.170	26.762	71.528	64.540	51.236	42.903	740.01	348.64	193.58	88.328
	0.3	22.248	21.373	20.365	18.846	34.464	32.183	29.797	26.185	71.528	61.564	53.508	41.009	740.01	282.80	237.39	79.512
	0.4	22.248	21.098	20.626	18.602	34.464	31493	30.434	25.617	71.528	58.870	55.856	39.190	740.01	239.86	288.20	77.693
	0.5	22.248	20.830	20.891	18.360	34.464	30.835	31.081	25.060	71.528	56.422	58.279	37.447	740.01	209.02	346.00	82.874
	0.6	22.248	20.569	21.157	18.120	34.464	30.206	31.738	24.513	71.528	54.187	60.777	35.779	740.01	185.44	410.81	95.052
	0.7	22.248	20.316	21.426	17.883	34.464	29.604	32.405	23.975	71.528	52.141	63.352	34.187	740.01	166.62	482.61	114.23
	0.8	22.248	20.069	21.698	17.649	34.464	29.028	33.081	23.448	71.528	50.259	66.001	32.671	740.01	151.14	561.41	140.41
	0.9	22.248	19.829	21.972	17.416	34.464	28.476	33.768	22.930	71.528	48.524	68.727	31.230	740.01	138.11	647.21	173.58
	1.0	22.248	19.594	22.248	17.187	34.464	27.946	34.464	22.422	71.528	46.919	71.528	29.864	740.01	126.96	740.01	213.75