Modified One-Parameter Liu Estimator for the Linear Regression Model

Table 7

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	0.0260	0.0259	0.0253	0.0252	0.0355	0.0354	0.0343	0.0341	0.0650	0.0645	0.0612	0.0604	0.5874	0.5532	0.3747	0.3374
	0.2	0.0260	0.0258	0.0254	0.0251	0.0355	0.0352	0.0344	0.0339	0.0650	0.0641	0.0616	0.0600	0.5874	0.5221	0.3947	0.3201
	0.3	0.0260	0.0257	0.0254	0.0250	0.0355	0.0351	0.0346	0.0338	0.0650	0.0636	0.0620	0.0597	0.5874	0.4940	0.4156	0.3038
	0.4	0.0260	0.0257	0.0255	0.0250	0.0355	0.0350	0.0347	0.0337	0.0650	0.0632	0.0624	0.0593	0.5874	0.4685	0.4374	0.2883
	0.5	0.0260	0.0256	0.0256	0.0249	0.0355	0.0348	0.0348	0.0336	0.0650	0.0628	0.0628	0.0589	0.5874	0.4452	0.4602	0.2737
	0.6	0.0260	0.0255	0.0257	0.0248	0.0355	0.0347	0.0350	0.0335	0.0650	0.0624	0.0632	0.0586	0.5874	0.4240	0.4838	0.2601
	0.7	0.0260	0.0254	0.0257	0.0248	0.0355	0.0346	0.0351	0.0334	0.0650	0.0620	0.0636	0.0582	0.5874	0.4046	0.5084	0.2473
	0.8	0.0260	0.0254	0.0258	0.0247	0.0355	0.0344	0.0352	0.0333	0.0650	0.0616	0.0641	0.0579	0.5874	0.3868	0.5338	0.2355
	0.9	0.0260	0.0253	0.0259	0.0247	0.0355	0.0343	0.0354	0.0331	0.0650	0.0612	0.0645	0.0576	0.5874	0.3705	0.5602	0.2246
	1.0	0.0260	0.0252	0.0260	0.0246	0.0355	0.0342	0.0355	0.0330	0.0650	0.0608	0.0650	0.0572	0.5874	0.3556	0.5874	0.2145
5	0.1	0.6208	0.6195	0.6089	0.6063	0.8560	0.8533	0.8322	0.8270	1.5796	1.5699	1.4957	1.4774	14.6151	13.7762	9.1902	8.1593
	0.2	0.6208	0.6181	0.6102	0.6050	0.8560	0.8506	0.8348	0.8244	1.5796	1.5603	1.5049	1.4684	14.6151	13.0082	9.7294	7.6677
	0.3	0.6208	0.6168	0.6115	0.6037	0.8560	0.8479	0.8374	0.8218	1.5796	1.5507	1.5141	1.4593	14.6151	12.3033	10.2845	7.1920
	0.4	0.6208	0.6155	0.6128	0.6024	0.8560	0.8453	0.8401	0.8192	1.5796	1.5413	1.5234	1.4503	14.6151	11.6549	10.8556	6.7321
	0.5	0.6208	0.6141	0.6142	0.6011	0.8560	0.8426	0.8427	0.8166	1.5796	1.5319	1.5327	1.4413	14.6151	11.0570	11.4424	6.2882
	0.6	0.6208	0.6128	0.6155	0.5998	0.8560	0.8400	0.8454	0.8140	1.5796	1.5227	1.5420	1.4324	14.6151	10.5045	12.0452	5.8601
	0.7	0.6208	0.6115	0.6168	0.5985	0.8560	0.8373	0.8480	0.8114	1.5796	1.5135	1.5513	1.4234	14.6151	9.9929	12.6639	5.4479
	0.8	0.6208	0.6102	0.6181	0.5972	0.8560	0.8347	0.8507	0.8088	1.5796	1.5045	1.5607	1.4146	14.6151	9.5184	13.2984	5.0515
	0.9	0.6208	0.6089	0.6195	0.5959	0.8560	0.8321	0.8533	0.8063	1.5796	1.4955	1.5702	1.4057	14.6151	9.0774	13.9488	4.6711
	1.0	0.6208	0.6076	0.6208	0.5946	0.8560	0.8296	0.8560	0.8037	1.5796	1.4866	1.5796	1.3969	14.6151	8.6668	14.6151	4.3065
10	0.1	2.4784	2.4731	2.4315	2.4211	3.4193	3.4086	3.3251	3.3044	6.3127	6.2741	5.9791	5.9063	58.4499	55.0988	36.7499	32.6162
	0.2	2.4784	2.4678	2.4367	2.4159	3.4193	3.3980	3.3355	3.2940	6.3127	6.2359	6.0157	5.8701	58.4499	52.0297	38.9107	30.6432
	0.3	2.4784	2.4626	2.4418	2.4108	3.4193	3.3874	3.3459	3.2837	6.3127	6.1980	6.0524	5.8340	58.4499	49.2118	41.1340	28.7328
	0.4	2.4784	2.4573	2.4470	2.4056	3.4193	3.3768	3.3563	3.2734	6.3127	6.1605	6.0893	5.7980	58.4499	46.6183	43.4199	26.8850
	0.5	2.4784	2.4521	2.4523	2.4005	3.4193	3.3664	3.3668	3.2631	6.3127	6.1233	6.1262	5.7621	58.4499	44.2260	45.7685	25.0998
	0.6	2.4784	2.4469	2.4575	2.3953	3.4193	3.3559	3.3773	3.2529	6.3127	6.0865	6.1633	5.7263	58.4499	42.0146	48.1796	23.3772
	0.7	2.4784	2.4417	2.4627	2.3902	3.4193	3.3456	3.3877	3.2426	6.3127	6.0500	6.2005	5.6907	58.4499	39.9662	50.6533	21.7172
	0.8	2.4784	2.4366	2.4679	2.3851	3.4193	3.3352	3.3982	3.2324	6.3127	6.0139	6.2378	5.6552	58.4499	38.0652	53.1896	20.1197
	0.9	2.4784	2.4314	2.4732	2.3800	3.4193	3.3250	3.4088	3.2222	6.3127	5.9781	6.2752	5.6198	58.4499	36.2978	55.7884	18.5849
	1.0	2.4784	2.4263	2.4784	2.3748	3.4193	3.3147	3.4193	3.2120	6.3127	5.9427	6.3127	5.5845	58.4499	34.6518	58.4499	17.1126