Modelling and Simulation in Engineering

Research Article

Modified One-Parameter Liu Estimator for the Linear Regression Model

Table 5

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	0.4876	0.4746	0.3942	0.3756	0.7704	0.7350	0.5473	0.5057	1.6417	1.4749	0.8662	0.7433	17.673	7.9846	1.9910	1.0357
	0.2	0.4876	0.4624	0.4038	0.3666	0.7704	0.7029	0.5693	0.4859	1.6417	1.3411	0.9343	0.6886	17.673	5.3441	2.8135	0.9031
	0.3	0.4876	0.4508	0.4136	0.3578	0.7704	0.6738	0.5919	0.4669	1.6417	1.2314	1.0070	0.6384	17.673	4.0252	3.8661	1.0004
	0.4	0.4876	0.4399	0.4236	0.3492	0.7704	0.6471	0.6152	0.4485	1.6417	1.1399	1.0842	0.5927	17.673	3.2147	5.1486	1.3276
	0.5	0.4876	0.4295	0.4338	0.3408	0.7704	0.6227	0.6393	0.4309	1.6417	1.0623	1.1659	0.5515	17.673	2.6636	6.6610	1.8849
	0.6	0.4876	0.4196	0.4441	0.3326	0.7704	0.6003	0.6641	0.4140	1.6417	0.9957	1.2520	0.5148	17.673	2.2653	8.4035	2.6720
	0.7	0.4876	0.4103	0.4547	0.3246	0.7704	0.5796	0.6896	0.3979	1.6417	0.9379	1.3427	0.4826	17.673	1.9654	10.376	3.6892
	0.8	0.4876	0.4014	0.4655	0.3167	0.7704	0.5604	0.7158	0.3824	1.6417	0.8873	1.4379	0.4549	17.673	1.7327	12.578	4.9363
	0.9	0.4876	0.3929	0.4764	0.3091	0.7704	0.5427	0.7428	0.3677	1.6417	0.8424	1.5375	0.4317	17.673	1.5479	15.011	6.4134
	1.0	0.4876	0.3849	0.4876	0.3016	0.7704	0.5261	0.7704	0.3537	1.6417	0.8025	1.6417	0.4130	17.673	1.3984	17.673	8.1205

5	0.1	12.190	11.866	9.8393	9.3648	19.261	18.376	13.650	12.589	41.042	36.874	21.539	18.403	441.82	199.51	47.225	22.001
	0.2	12.190	11.560	10.083	9.1341	19.261	17.573	14.206	12.084	41.042	33.525	23.270	16.999	441.82	133.20	68.355	17.906
	0.3	12.190	11.270	10.331	8.9077	19.261	16.842	14.779	11.595	41.042	30.775	25.110	15.704	441.82	99.857	95.164	19.490
	0.4	12.190	10.994	10.584	8.6856	19.261	16.174	15.369	11.124	41.042	28.475	27.059	14.517	441.82	79.213	127.65	26.753
	0.5	12.190	10.733	10.841	8.4680	19.261	15.560	15.975	10.669	41.042	26.522	29.117	13.440	441.82	65.056	165.82	39.694
	0.6	12.190	10.733	10.841	8.4679	19.261	14.994	16.598	10.232	41.042	24.840	31.284	12.471	441.82	54.734	209.66	58.313
	0.7	12.190	10.733	10.841	8.4680	19.261	14.470	17.239	9.8108	41.042	23.375	33.560	11.612	441.82	46.888	259.18	82.611
	0.8	12.190	10.484	11.102	8.2545	19.261	13.985	17.896	9.4068	41.042	22.086	35.945	10.861	441.82	40.740	314.38	112.59
	0.9	12.190	10.248	11.367	8.0455	19.261	13.533	18.570	9.0197	41.042	20.941	38.439	10.220	441.82	35.807	375.26	148.24
	1.0	12.190	9.5999	12.190	7.4446	19.261	13.111	19.261	8.6495	41.042	19.917	41.042	9.6868	441.82	31.774	441.82	189.58

10	0.1	48.759	47.464	39.357	37.458	77.044	73.503	54.600	50.354	164.17	147.50	86.148	73.599	1767.3	798.06	188.64	87.571
	0.2	48.759	46.239	40.333	36.535	77.044	70.294	56.824	48.331	164.17	134.10	93.076	67.978	1767.3	532.77	273.23	71.092
	0.3	48.759	45.079	41.325	35.629	77.044	67.370	59.116	46.377	164.17	123.10	100.44	62.791	1767.3	399.37	380.53	77.317
	0.4	48.759	43.978	42.335	34.740	77.044	64.696	61.475	44.489	164.17	113.90	108.24	58.041	1767.3	316.75	510.52	106.245
	0.5	48.759	42.933	43.363	33.868	77.044	62.240	63.901	42.669	164.17	106.09	116.47	53.725	1767.3	260.08	663.22	157.88
	0.6	48.759	41.938	44.407	33.014	77.044	59.976	66.395	40.917	164.17	99.359	125.14	49.845	1767.3	218.75	838.63	232.21
	0.7	48.759	40.991	45.469	32.177	77.044	57.882	68.956	39.231	164.17	93.497	134.24	46.400	1767.3	187.32	1036.7	329.25
	0.8	48.759	40.087	46.548	31.357	77.044	55.939	71.584	37.613	164.17	88.338	143.78	43.390	1767.3	162.69	1257.6	449.00
	0.9	48.759	39.224	47.645	30.555	77.044	54.131	74.280	36.063	164.17	83.757	153.76	40.816	1767.3	142.92	1501.1	591.44
	1.0	48.759	38.399	48.759	29.770	77.044	52.443	77.044	34.580	164.17	79.656	164.17	38.677	1767.3	126.75	1767.3	756.59