Modified One-Parameter Liu Estimator for the Linear Regression Model

Table 4

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	0.8375	0.8019	0.6073	0.5645	1.3038	1.2137	0.8030	0.7166	2.7626	2.3689	1.1868	0.9622	30.134	10.720	2.2263	0.9170
	0.2	0.8375	0.7694	0.6299	0.5442	1.3038	1.1356	0.8496	0.6767	2.7626	2.0758	1.3162	0.8670	30.134	6.4830	3.5481	0.9295
	0.3	0.8375	0.7395	0.6532	0.5246	1.3038	1.0673	0.8985	0.6392	2.7626	1.8492	1..4571	0.7833	30.134	4.5630	5.3147	1.3867
	0.4	0.8375	0.7121	0.6773	0.5058	1.3038	1.0072	0.9496	0.6039	2.7626	1.6691	1.6093	0.7109	30.134	3.4720	7.5260	2.2886
	0.5	0.8375	0.6868	0.7021	0.4877	1.3038	0.9539	1.0030	0.5708	2.7626	1.5224	1.7730	0.6500	30.134	2.7762	10.182	3.6354
	0.6	0.8375	0.6635	0.7277	0.4705	1.3038	0.9063	1.0586	0.5400	2.7626	1.4006	1.9481	0.6005	30.134	2.2996	13.283	5.4268
	0.7	0.8375	0.6418	0.7540	0.4539	1.3038	0.8636	1.1166	0.5115	2.7626	1.2980	2.1346	0.5624	30.134	1.9565	16.828	7.6631
	0.8	0.8375	0.6217	0.7811	0.4381	1.3038	0.8252	1.1767	0.4853	2.7626	1.2104	2.3325	0.5357	30.134	1.7004	20.819	10.344
	0.9	0.8375	0.6030	0.8089	0.4231	1.3038	0.7903	1.2391	0.4613	2.7626	1.1348	2.5418	0.5204	30.134	1.5038	25.254	13.470
	1.0	0.8375	0.5855	0.8375	0.4088	1.3038	0.7587	1.3038	0.4395	2.7626	1.0688	2.7626	0.5166	30.134	1.3493	30.134	17.040
5	0.1	20.936	20.040	15.024	13.885	32.596	30.329	19.803	17.525	69.065	59.182	29.022	23.128	753.34	266.98	50.691	15.905
	0.2	20.936	19.216	15.618	13.339	32.596	28.357	21.019	16.463	69.065	51.794	32.378	20.591	753.34	160.14	84.633	15.061
	0.3	20.936	18.457	16.227	12.809	32.596	26.624	22.286	15.452	69.065	46.060	36.008	18.328	753.34	111.36	129.61	25.249
	0.4	20.936	17.755	16.852	12.295	32.596	25.091	23.605	14.493	69.065	41.478	39.911	16.337	753.34	83.415	185.61	46.470
	0.5	20..936	17.104	17.493	11.797	32.596	23.724	24.975	13.586	69.065	37.727	44.087	14.620	753.34	65.445	252.65	78.724
	0.6	20.936	16.498	18.150	11.315	32.596	22.498	26.396	12.729	69.065	34.597	48.536	14.176	753.34	53.028	330.73	122.01
	0.7	20.936	15.933	18.823	10.848	32.596	21.392	27.869	11.924	69.065	31.943	53.258	12.005	753.34	44.012	419.83	176.33
	0.8	20.936	15.405	19.512	10.398	32.596	20.389	29.393	11.171	69.065	29.662	58.254	11.107	753.34	37.220	519.97	241.68
	0.9	20.936	14.911	20.216	9.9630	32.596	19.474	30.969	10.469	69.065	27.679	63.523	10.482	753.34	31.956	631.14	318.06
	1.0	20.936	14.447	20.936	9.5441	32.596	18.638	32.596	9.8179	69.065	25.938	69.065	10.131	753.34	27.782	753.34	405.48
10	0.1	83.746	80.157	60.064	55.497	130.38	121.31	79.156	70.028	276.26	236.71	115.97	92.358	3013.4	1067.6	201.97	62.631
	0.2	83.746	76.859	62.443	53.307	130.38	113.42	84.028	65.771	276.26	207.15	129.41	82.190	3013.4	640.15	337.83	59.156
	0.3	83.746	73.819	64.885	51.181	130.38	106.48	89.105	61.719	276.26	184.20	143.95	73.113	3013.4	444.94	517.82	99.809
	0.4	83.746	71.006	67.390	49.118	130.38	100.34	94.387	57.872	276.26	165.85	159.57	65.129	3013.4	333.07	741.94	184.59
	0.5	83.746	68.397	69.958	47.119	130.38	94.868	99.874	54.230	276.26	150.84	176.29	58.236	3013.4	261.12	1010.2	313.50
	0.6	83.746	65.970	72.589	45.182	130.38	89.957	105.57	50.793	276.26	138.30	194.10	52.434	3013.4	211.39	1322.6	486.54
	0.7	83.746	63.707	75.284	43.309	130.38	85.526	111.46	47.561	276.26	127.67	213.00	47.725	3013.4	175.28	1679.1	703.71
	0.8	83.746	61.592	78.041	41.498	130.38	81.506	117.56	44.534	276.26	118.54	233.00	44.107	3013.4	148.06	2079.7	965.01
	0.9	83.746	59.610	80.862	39.751	130.38	77.842	123.87	41.712	276.26	110.59	254.08	41.581	3013.4	126.97	2524.5	1270.4
	1.0	83.746	57.749	83.746	38.067	130.38	74.490	130.38	39.095	276.26	103.62	276.26	40.147	3013.4	110.24	3013.4	1620.0