Mathematical Problems in Engineering

Research Article

Modified Robust Ridge M-Estimators in Two-Parameter Ridge Regression Model

Table 13

Estimated MSE for n = 20, , and 20% outlier in the y-direction.


Correlation (δ²)	Error variance (σ²)	OLS	M	RE	MRE	M1	TRME1	MTPM1	MTPM2	MTPM3	TRME2	MTPM4	MTPM5	MTPM6

0.85	0.1	273.4793	156.7689	206.1094	86.1653	77.0995	43.6674	21.6971	87.8649	113.8645	36.1357	40.114	67.8668	86.8745
	1	273.0539	157.4089	205.5957	86.2185	77.1741	42.9368	21.7251	87.9107	114.0479	35.8279	40.0981	67.7972	86.823
	5	275.4729	157.4634	205.4779	85.6156	76.837	37.7866	20.6376	80.175	110.7684	31.3609	35.0601	58.2451	75.305
	10	286.5291	182.217	209.3173	98.923	87.2395	43.8661	23.8501	90.6212	127.5594	33.3307	39.2086	64.0506	83.212

0.95	0.1	819.1836	455.426	612.785	246.591	221.5231	127.5565	53.7494	315.4418	325.2237	92.1506	105.9181	226.5454	284.7621
	1	819.9241	459.3204	613.2985	247.6881	222.4191	125.7323	54.2189	317.7502	327.5723	90.9346	107.0494	228.1556	286.9329
	5	827.7403	462.5611	613.419	248.1087	222.9635	109.3106	55.1827	301.6026	321.9096	81.5994	100.7558	208.9254	263.933
	10	860.5311	534.6709	623.4981	283.2951	249.8283	120.6435	60.6973	337.4342	368.3171	85.6961	109.0555	225.2578	288.8946

0.99	0.1	3901.296	2150.331	2901.249	1165.627	1051.513	624.9954	231.795	1534.714	1517.236	434.0425	400.8136	1227.798	1467.73
	1	3901.224	2167.916	2899.996	1170.029	1055.25	614.6947	233.3161	1544.155	1526.87	427.0813	407.4048	1238.502	1477.911
	5	3930.612	2169.253	2892.813	1168.533	1054.01	531.9327	250.3252	1499.776	1491.422	371.725	431.5145	1200.767	1410.728
	10	4093.132	2522.274	2942.757	1339.398	1184.609	580.171	276.6247	1721.755	1716.665	388.6839	475.891	1319.492	1580.715

0.999	0.1	34369.11	20559.64	25211.45	11310.83	10175.82	6176.912	2128.203	14561.13	14550.91	4296.599	2775.708	13400.44	14661.01
	1	34395.97	20732.63	25226.4	11355.68	10211.26	6092.753	2131.213	14663.9	14653.83	4227.387	2803.213	13509.58	14757.11
	5	34854.44	20888.84	25348.75	11428.23	10263.13	5268.545	2313.528	14461.07	14455.43	3601.397	3343.458	13395.13	14349.82
	10	35984.14	24046.08	25578.88	13055.78	11492.34	5758.728	2525.172	16536.65	16525.08	3696.633	3712.092	14860.09	16222.84