Modified One-Parameter Liu Estimator for the Linear Regression Model

Table 8

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	0.0608	0.0607	0.0598	0.0595	0.0856	0.0854	0.0835	0.0830	0.1620	0.1611	0.1543	0.1527	1.5604	1.4782	1.0328	0.9358
	0.2	0.0608	0.0606	0.0599	0.0594	0.0856	0.0851	0.0837	0.0828	0.1620	0.1602	0.1552	0.1519	1.5604	1.4031	1.0840	0.8901
	0.3	0.0608	0.0605	0.0600	0.0593	0.0856	0.0849	0.0839	0.0825	0.1620	0.1593	0.1560	0.1511	1.5604	1.3343	1.1371	0.8463
	0.4	0.0608	0.0603	0.0601	0.0592	0.0856	0.0846	0.0842	0.0823	0.1620	0.1585	0.1568	0.1504	1.5604	1.2712	1.1921	0.8042
	0.5	0.0608	0.0602	0.0602	0.0591	0.0856	0.0844	0.0844	0.0821	0.1620	0.1576	0.1577	0.1496	1.5604	1.2132	1.2488	0.7641
	0.6	0.0608	0.0601	0.0603	0.0590	0.0856	0.0841	0.0846	0.0819	0.1620	0.1568	0.1585	0.1488	1.5604	1.1598	1.3075	0.7257
	0.7	0.0608	0.0600	0.0605	0.0589	0.0856	0.0839	0.0849	0.0817	0.1620	0.1559	0.1594	0.1481	1.5604	1.1105	1.3679	0.6892
	0.8	0.0608	0.0599	0.0606	0.0588	0.0856	0.0837	0.0851	0.0815	0.1620	0.1551	0.1602	0.1473	1.5604	1.0649	1.4302	0.6546
	0.9	0.0608	0.0598	0.0607	0.0587	0.0856	0.0834	0.0854	0.0812	0.1620	0.1543	0.1611	0.1466	1.5604	1.0226	1.4944	0.6218
	1.0	0.0608	0.0596	0.0608	0.0586	0.0856	0.0832	0.0856	0.0810	0.1620	0.1535	0.1620	0.1459	1.5604	0.9834	1.5604	0.5908
5	0.1	1.5209	1.5177	1.4931	1.4869	2.1402	2.1338	2.0844	2.0722	4.0504	4.0274	3.8518	3.8085	39.0100	36.9446	25.4493	22.8472
	0.2	1.5209	1.5146	1.4961	1.4839	2.1402	2.1275	2.0906	2.0660	4.0504	4.0047	3.8736	3.7869	39.0100	35.0465	26.8065	21.6023
	0.3	1.5209	1.5115	1.4992	1.4808	2.1402	2.1213	2.0967	2.0599	4.0504	3.9822	3.8954	3.7654	39.0100	33.2972	28.2010	20.3948
	0.4	1.5209	1.5084	1.5023	1.4778	2.1402	2.1150	2.1029	2.0539	4.0504	3.9598	3.9174	3.7440	39.0100	31.6813	29.6329	19.2247
	0.5	1.5209	1.5053	1.5054	1.4747	2.1402	2.1088	2.1091	2.0478	4.0504	3.9377	3.9393	3.7226	39.0100	30.1850	31.1023	18.0919
	0.6	1.5209	1.5022	1.5085	1.4717	2.1402	2.1027	2.1153	2.0417	4.0504	3.9158	3.9614	3.7013	39.0100	28.7964	32.6090	16.9966
	0.7	1.5209	1.4991	1.5116	1.4686	2.1402	2.0965	2.1215	2.0357	4.0504	3.8941	3.9835	3.6801	39.0100	27.5052	34.1531	15.9387
	0.8	1.5209	1.4961	1.5147	1.4656	2.1402	2.0904	2.1277	2.0296	4.0504	3.8726	4.0057	3.6590	39.0100	26.3022	35.7347	14.9181
	0.9	1.5209	1.4930	1.5178	1.4626	2.1402	2.0843	2.1339	2.0236	4.0504	3.8512	4.0280	3.6379	39.0100	25.1794	37.3536	13.9350
	1.0	1.5209	1.4900	1.5209	1.4595	2.1402	2.0783	2.1402	2.0175	4.0504	3.8301	4.0504	3.6169	39.0100	24.1296	39.0100	12.9893
10	0.1	6.0835	6.0709	5.9721	5.9475	8.5606	8.5353	8.3373	8.2882	16.2015	16.1096	15.4061	15.2323	156.0399	147.7764	101.7462	91.3151
	0.2	6.0835	6.0584	5.9844	5.9352	8.5606	8.5101	8.3620	8.2636	16.2015	16.0186	15.4934	15.1457	156.0399	140.1802	107.1845	86.3224
	0.3	6.0835	6.0459	5.9967	5.9230	8.5606	8.4850	8.3867	8.2392	16.2015	15.9284	15.5810	15.0595	156.0399	133.1789	112.7715	81.4783
	0.4	6.0835	6.0335	6.0091	5.9107	8.5606	8.4600	8.4114	8.2147	16.2015	15.8390	15.6688	14.9735	156.0399	126.7096	118.5070	76.7827
	0.5	6.0835	6.0211	6.0214	5.8985	8.5606	8.4352	8.4362	8.1903	16.2015	15.7504	15.7569	14.8878	156.0399	120.7180	124.3910	72.2358
	0.6	6.0835	6.0088	6.0338	5.8863	8.5606	8.4105	8.4610	8.1659	16.2015	15.6626	15.8453	14.8024	156.0399	115.1568	130.4237	67.8373
	0.7	6.0835	5.9965	6.0462	5.8741	8.5606	8.3859	8.4858	8.1416	16.2015	15.5756	15.9339	14.7172	156.0399	109.9844	136.6049	63.5875
	0.8	6.0835	5.9842	6.0586	5.8619	8.5606	8.3614	8.5107	8.1173	16.2015	15.4893	16.0229	14.6323	156.0399	105.1643	142.9346	59.4862
	0.9	6.0835	5.9720	6.0710	5.8497	8.5606	8.3370	8.5356	8.0931	16.2015	15.4038	16.1120	14.5476	156.0399	100.6645	149.4130	55.5334
	1.0	6.0835	5.9598	6.0835	5.8375	8.5606	8.3127	8.5606	8.0689	16.2015	15.3190	16.2015	14.4633	156.0399	96.4563	156.0399	51.7293