Modelling and Simulation in Engineering

Research Article

Modified One-Parameter Liu Estimator for the Linear Regression Model

Table 3

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	0.1124	0.1121	0.1105	0.1103	0.1492	0.1478	0.1396	0.1380	0.2867	0.2781	0.2304	0.2209	3.0721	2.1409	0.6883	0.4808
	0.2	0.1124	0.1118	0.1107	0.1102	0.1492	0.1465	0.1404	0.1372	0.2867	0.2702	0.2356	0.2165	3.0721	1.6206	0.8360	0.4210
	0.3	0.1124	0.1116	0.1108	0.1101	0.1492	0.1453	0.1414	0.1365	0.2867	0.2629	0.2410	0.2124	3.0721	1.2979	1.0130	0.3905
	0.4	0.1124	0.1114	0.1110	0.1100	0.1492	0.1442	0.1423	0.1358	0.2867	0.2562	0.2468	0.2086	3.0721	1.0825	1.2192	0.3893
	0.5	0.1124	0.1112	0.1112	0.1100	0.1492	0.1432	0.1434	0.1352	0.2867	0.2501	0.2527	0.2050	3.0721	0.9305	1.4548	0.4174
	0.6	0.1124	0.111	0.1114	0.1100	0.1492	0.1422	0.1444	0.1346	0.2867	0.2444	0.2590	0.2017	3.0721	0.8186	1.7197	0.4748
	0.7	0.1124	0.1108	0.1116	0.1099	0.1492	0.1412	0.1455	0.1341	0.2867	0.2391	0.2655	0.1987	3.0721	0.7333	2.0138	0.5615
	0.8	0.1124	0.1106	0.1119	0.1099	0.1492	0.1403	0.1467	0.1336	0.2867	0.2342	0.2723	0.1959	3.0721	0.6667	2.3373	0.6775
	0.9	0.1124	0.1105	0.1121	0.1099	0.1492	0.1395	0.1479	0.1332	0.2867	0.2297	0.2793	0.1934	3.0721	0.6134	2.6900	0.8228
	1.0	0.1124	0.1104	0.1124	0.1099	0.1492	0.1387	0.1492	0.1328	0.2867	0.2255	0.2867	0.1912	3.0721	0.5699	3.0721	0.9973

5	0.1	2.0631	2.0452	1.9126	1.8802	3.2440	3.1954	2.8523	2.7697	6.9576	6.7191	5.2564	4.9172	76.772	53.314	14.747	8.2979
	0.2	2.0631	2.0276	1.9289	1.8642	3.2440	3.1480	2.8942	2.7290	6.9576	6.4945	5.4313	4.7529	76.772	39.906	18.971	6.0738
	0.3	2.0631	2.0102	1.9454	1.8483	3.2440	3.1019	2.9365	2.6887	6.9576	6.2827	5.6097	4.5921	76.772	31.412	23.862	4.5166
	0.4	2.0631	1.9932	1.9619	1.8325	3.2440	3.0570	2.9793	2.6487	6.9576	6.0826	5.7917	4.4349	76.772	25.626	29.420	3.6261
	0.5	2.0631	1.9764	1.9785	1.8167	3.2440	3.0133	3.0224	2.6092	6.9576	5.8934	5.9772	4.2811	76.772	21.466	35.645	3.4025
	0.6	2.0631	1.9599	1.9952	1.8011	3.2440	2.9707	3.0659	2.5701	6.9576	5.7143	6.1662	4.1310	76.772	18.350	42.537	3.8457
	0.7	2.0631	1.9436	2.0121	1.7856	3.2440	2.9291	3.1098	2.5314	6.9576	5.5445	6.3587	3.9843	76.772	15.939	50.096	4.9557
	0.8	2.0631	1.9276	2.029	1.7702	3.2440	2.8887	3.1542	2.4931	6.9576	5.3834	6.5548	3.8412	76.772	14.024	58.321	6.7325
	0.9	2.0631	1.9119	2.0460	1.7548	3.2440	2.8492	3.1989	2.4553	6.9576	5.2305	6.7544	3.7016	76.772	12.471	67.213	9.1762
	1.0	2.0631	1.8964	2.0631	1.7396	3.2440	2.8108	3.2440	2.4178	6.9576	5.0850	6.9576	3.5656	76.772	11.189	76.772	12.287

10	0.1	8.1632	8.0901	7.5481	7.4154	12.920	12.723	11.334	10.999	27.809	26.853	20.970	19.601	307.09	213.26	58.717	32.755
	0.2	8.1632	8.0182	7.615	7.3496	12.920	12.532	11.505	10.833	27.809	25.951	21.675	18.937	307.09	159.58	75.684	23.760
	0.3	8.1632	7.9474	7.6822	7.2842	12.920	12.346	11.676	10.669	27.809	25.100	22.394	18.287	307.09	125.56	95.308	17.423
	0.4	8.1632	7.8777	7.7498	7.2191	12.920	12.164	11.849	10.507	27.809	24.296	23.126	17.650	307.09	102.37	117.59	13.743
	0.5	8.1632	7.8091	7.8178	7.1544	12.920	11.987	12.024	10.346	27.809	23.535	23.872	17.028	307.09	85.681	142.53	12.721
	0.6	8.1632	7.7415	7.8862	7.0901	12.920	11.814	12.200	10.186	27.809	22.815	24.632	16.419	307.09	73.175	170.13	14.356
	0.7	8.1632	7.675	7.9549	7.0261	12.920	11.646	12.378	10.028	27.809	22.131	25.406	15.823	307.09	63.493	200.38	18.648
	0.8	8.1632	7.6096	8.0240	6.9625	12.920	11.4821	12.557	9.8717	27.809	21.482	26.193	15.242	307.09	55.802	233.29	25.598
	0.9	8.1632	7.5451	8.0934	6.8992	12.920	11.322	12.738	9.7168	27.809	20.865	26.994	14.674	307.09	49.561	268.86	35.206
	1.0	8.1632	7.4816	8.1632	6.8364	12.920	11.166	12.920	9.5634	27.809	20.279	27.809	14.120	307.09	44.407	307.09	47.470