Modelling and Simulation in Engineering

Research Article

Modified One-Parameter Liu Estimator for the Linear Regression Model

Table 2

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	0.1336	0.1325	0.1249	0.1232	0.1806	0.1785	0.1646	0.1614	0.3253	0.3172	0.2685	0.2577	2.8206	2.1349	0.7453	0.5194
	0.2	0.1336	0.1314	0.1258	0.1224	0.1806	0.1765	0.1662	0.1599	0.3253	0.3097	0.2741	0.2526	2.8206	1.6977	0.8903	0.4386
	0.3	0.1336	0.1304	0.1267	0.1216	0.1806	0.1746	0.1679	0.1584	0.3253	0.3025	0.2799	0.2477	2.8206	1.3996	1.0568	0.3791
	0.4	0.1336	0.1294	0.1277	0.1208	0.1806	0.1727	0.1696	0.1570	0.3253	0.2958	0.2859	0.2429	2.8206	1.1861	1.2446	0.3410
	0.5	0.1336	0.1285	0.1286	0.1200	0.1806	0.1709	0.1713	0.1556	0.3253	0.2895	0.2920	0.2383	2.8206	1.0274	1.4538	0.3243
	0.6	0.1336	0.1275	0.1296	0.1192	0.1806	0.1692	0.1731	0.1542	0.3253	0.2836	0.2983	0.2339	2.8206	0.9058	1.6844	0.3289
	0.7	0.1336	0.1266	0.1305	0.1185	0.1806	0.1676	0.1749	0.1529	0.3253	0.2780	0.3048	0.2297	2.8206	0.8105	1.9363	0.3550
	0.8	0.1336	0.1257	0.1315	0.1177	0.1806	0.1660	0.1767	0.1516	0.3253	0.2727	0.3115	0.2256	2.8206	0.7344	2.2097	0.4025
	0.9	0.1336	0.1249	0.1325	0.1170	0.1806	0.1644	0.1786	0.1504	0.3253	0.2677	0.3183	0.2217	2.8206	0.6726	2.5044	0.4713
	1	0.1336	0.1241	0.1336	0.1163	0.1806	0.1630	0.1806	0.1491	0.3253	0.2630	0.3253	0.2180	2.8206	0.6217	2.8206	0.5615

5	0.1	3.0492	3.0174	2.7831	2.7259	4.1707	4.1067	3.6537	3.5443	7.5964	7.3662	5.9057	5.5633	69.766	52.391	15.944	9.5391
	0.2	3.0492	2.9860	2.8119	2.6976	4.1707	4.0443	3.7092	3.4904	7.5964	7.1477	6.0815	5.3966	69.766	41.181	19.904	7.0945
	0.3	3.0492	2.9553	2.8410	2.6695	4.1707	3.9836	3.7651	3.4370	7.5964	6.9399	6.2603	5.2329	69.766	33.446	24.369	5.1550
	0.4	3.0492	2.9251	2.8702	2.6415	4.1707	3.9244	3.8216	3.3840	7.5964	6.7421	6.4421	5.0723	69.766	27.840	29.339	3.7205
	0.5	3.0492	2.8954	2.8996	2.6138	4.1707	3.8667	3.8785	3.3315	7.5964	6.5538	6.6269	4.9146	69.766	23.620	34.814	2.7912
	0.6	3.0492	2.8662	2.9291	2.5862	4.1707	3.8104	3.9360	3.2796	7.5964	6.3742	6.8148	4.7601	69.766	20.350	40.794	2.3669
	0.7	3.0492	2.8375	2.9589	2.5588	4.1707	3.7555	3.9939	3.2281	7.5964	6.2028	7.0056	4.6085	69.766	17.755	47.280	2.4478
	0.8	3.0492	2.8094	2.9888	2.5315	4.1707	3.7020	4.0523	3.1771	7.5964	6.0391	7.1995	4.4599	69.766	15.655	54.270	3.0337
	0.9	3.0492	2.7817	3.0189	2.5045	4.1707	3.6498	4.1113	3.1267	7.5964	5.8826	7.3965	4.3144	69.766	13.929	61.766	4.1247
	1	3.0492	2.7544	3.0492	2.4776	4.1707	3.5988	4.1707	3.0767	7.5964	5.7330	7.5964	4.1719	69.766	12.489	69.767	5.7209

10	0.1	12.177	12.049	11.108	10.877	16.661	16.404	14.582	14.141	30.351	29.427	23.561	22.182	279.07	209.56	63.558	37.824
	0.2	12.177	11.923	11.224	10.763	16.661	16.154	14.805	13.923	30.351	28.550	24.267	21.511	279.07	164.70	79.447	27.978
	0.3	12.177	11.800	11.340	10.650	16.661	15.909	15.030	13.707	30.351	27.716	24.986	20.852	279.07	133.72	97.350	20.146
	0.4	12.177	11.678	11.458	10.537	16.661	15.671	15.257	13.494	30.351	26.922	25.717	20.205	279.07	111.26	117.27	14.328
	0.5	12.177	11.559	11.576	10.425	16.661	15.439	15.487	13.282	30.351	26.166	26.459	19.569	279.07	94.352	139.20	10.525
	0.6	12.177	11.442	11.695	10.314	16.661	15.213	15.718	13.072	30.351	25.444	27.214	18.945	279.07	81.240	163.14	8.7356
	0.7	12.177	11.327	11.814	10.204	16.661	14.992	15.951	12.864	30.351	24.755	27.980	18.334	279.07	70.829	189.10	8.9606
	0.8	12.177	11.213	11.934	10.094	16.661	14.776	16.186	12.658	30.351	24.097	28.758	17.734	279.07	62.401	217.08	11.200
	0.9	12.177	11.102	12.055	9.9840	16.661	14.566	16.423	12.454	30.351	23.468	29.548	17.146	279.07	55.468	247.06	15.453
	1	12.177	10.992	12.177	9.8760	16.661	14.360	16.661	12.252	30.351	22.866	30.351	16.570	279.07	49.684	279.07	21.721