Modelling and Simulation in Engineering

Research Article

Modified One-Parameter Liu Estimator for the Linear Regression Model

Table 1

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	0.3621	0.3517	0.2909	0.2782	0.5473	0.5186	0.3750	0.3461	1.1540	1.0117	0.5323	0.4458	12.774	4.1554	0.8567	0.3894
	0.2	0.3621	0.3420	0.2977	0.2722	0.5473	0.4929	0.3908	0.3329	1.1540	0.8995	0.5826	0.4096	12.774	2.3395	1.3877	0.4531
	0.3	0.3621	0.3329	0.3047	0.2666	0.5473	0.4699	0.4073	0.3206	1.1540	0.8094	0.6376	0.3781	12.774	1.6033	2.1170	0.7151
	0.4	0.3621	0.3245	0.3121	0.2612	0.5473	0.4493	0.4248	0.3092	1.1540	0.736	0.6973	0.3513	12.774	1.2143	3.0446	1.1753
	0.5	0.3621	0.3167	0.3197	0.2561	0.5473	0.4306	0.4431	0.2985	1.1540	0.6754	0.7617	0.3292	12.774	0.9779	4.1705	1.8339
	0.6	0.3621	0.3093	0.3276	0.2513	0.5473	0.4137	0.4622	0.2888	1.1540	0.6247	0.8307	0.3117	12.774	0.8214	5.4946	2.6906
	0.7	0.3621	0.3025	0.3358	0.2468	0.5473	0.3991	0.4822	0.2799	1.1540	0.5819	0.9045	0.2990	12.774	0.7117	7.0169	3.7457
	0.8	0.3621	0.2961	0.3443	0.2425	0.5473	0.3845	0.5031	0.2718	1.1540	0.5454	0.9830	0.2910	12.774	0.6314	8.7375	4.9990
	0.9	0.3621	0.29	0.353	0.2385	0.5473	0.3718	0.5248	0.2646	1.1540	0.5139	1.0661	0.2876	12.774	0.5708	10.656	6.4505
	1.0	0.3621	0.2844	0.3621	0.2348	0.5473	0.3601	0.5473	0.2583	1.1540	0.4867	1.1540	0.2890	12.774	0.5239	12.774	8.1003

5	0.1	8.0209	7.7585	6.1372	5.7600	12.967	12.232	8.3642	7.5029	28.462	24.840	12.067	9.5146	319.35	102.39	17.451	4.1230
	0.2	8.0209	7.5109	6.3314	5.5771	12.967	11.567	8.8169	7.0943	28.462	21.945	13.492	8.3869	319.35	56.008	31.445	4.7897
	0.3	8.0209	7.2770	6.5294	5.3980	12.967	10.962	9.2843	6.7003	28.462	19.588	15.017	7.3584	319.35	36.978	50.327	10.344
	0.4	8.0209	7.0557	6.7311	5.2226	12.967	10.411	9.7664	6.321	28.462	17.641	16.640	6.4290	319.35	26.816	74.095	20.784
	0.5	8.0209	6.8461	6.9367	5.0510	12.967	9.9071	10.263	5.9564	28.462	16.010	18.362	5.5988	319.35	20.580	102.75	36.112
	0.6	8.0209	6.6474	7.146	4.8832	12.967	9.4445	10.775	5.6065	28.462	14.627	20.184	4.8677	319.35	16.415	136.29	56.327
	0.7	8.0209	6.4588	7.3591	4.7192	12.967	9.0189	11.301	5.2713	28.462	13.442	22.105	4.2357	319.35	13.467	174.72	81.429
	0.8	8.0209	6.2795	7.5759	4.5589	12.967	8.6262	11.842	4.9508	28.462	12.418	24.124	3.7028	319.35	11.293	218.04	111.42
	0.9	8.0209	6.1090	7.7953	4.4024	12.967	8.2630	12.397	4.6450	28.462	11.526	26.243	3.2691	319.35	9.6369	266.24	146.30
	1.0	8.0209	5.9467	8.0209	4.2497	12.967	7.9262	12.967	4.3538	28.462	10.741	28.462	2.9345	319.35	8.3433	319.33	186.06

10	0.1	31.993	30.939	24.421	22.901	51.819	48.871	33.333	29.865	113.84	99.331	48.088	37.822	1277.4	409.25	69.149	15.713
	0.2	31.993	29.945	25.203	22.163	51.819	46.201	35.155	28.218	113.84	87.726	53.814	33.282	1277.4	223.57	125.20	18.323
	0.3	31.993	29.005	26.000	21.440	51.819	43.775	37.034	26.629	113.84	78.278	59.935	29.137	1277.4	147.37	200.79	40.484
	0.4	31.993	28.116	26.812	20.731	51.819	41.561	38.972	25.098	113.84	70.466	66.450	25.387	1277.4	106.67	295.94	82.197
	0.5	31.993	27.274	27.639	20.038	51.819	39.536	40.968	23.626	113.84	63.919	73.361	22.031	1277.4	81.687	410.64	143.46
	0.6	31.993	26.474	28.480	19.359	51.819	37.677	43.022	22.211	113.84	58.368	80.667	19.071	1277.4	64.998	544.90	224.28
	0.7	31.993	25.715	29.336	18.695	51.819	35.966	45.134	20.855	113.84	53.612	88.368	16.506	1277.4	53.189	698.70	324.65
	0.8	31.993	24.994	30.207	18.045	51.819	34.387	47.304	19.557	113.84	49.498	96.464	14.336	1277.4	44.476	872.06	444.57
	0.9	31.993	24.307	31.092	17.411	51.819	32.926	49.533	18.316	113.84	45.910	104.96	12.562	1277.4	37.839	1065.0	584.04
	1.0	31.993	23.654	31.993	16.791	51.819	31.570	51.819	17.134	113.84	42.758	113.84	11.182	1277.4	32.655	1277.4	743.07