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

Table 1

Estimated MSE for n = 20, , and 10% outlier in the y-direction.

Correlation (δ^2)	Error variance (σ^2)	OLS	M	RE	MRE	M1	TRME1	MTPM1	MTPM2	MTPM3	TRME2	MTPM4	MTPM5	MTPM6
0.85	0.1	29.9274	0.0502	23.2404	0.0261	0.0216	0.0106	0.0083	0.0085	0.0231	0.0089	0.0084	0.0084	0.0086
	1	29.9445	0.1417	23.2420	0.0632	0.0495	0.0288	0.0093	0.0131	0.0774	0.0127	0.0094	0.0103	0.0127
	5	30.4298	3.3915	23.1925	1.7838	1.5059	1.4681	0.6818	1.4220	2.2634	0.7886	0.7381	0.9542	1.3006
	10	32.4434	13.1172	23.6350	7.1191	6.0915	6.2093	3.3007	7.0652	8.8103	3.3957	3.6493	4.8688	6.4071
0.95	0.1	97.1115	0.1181	74.8629	0.0517	0.0401	0.0204	0.0064	0.0099	0.0752	0.0087	0.0064	0.0069	0.0091
	1	97.2380	0.4375	74.9289	0.1990	0.1578	0.1251	0.0313	0.0915	0.2865	0.0499	0.0323	0.0428	0.0737
	5	98.3760	10.7958	74.2675	5.6184	4.7191	4.8034	1.8124	6.1413	7.1779	2.3344	2.0383	3.3799	5.1130
	10	105.4989	42.3045	76.3297	22.4123	18.9711	19.9321	8.0798	27.0598	28.2246	9.4586	9.7093	17.0666	23.7698
0.99	0.1	494.5338	0.6391	378.7278	0.4060	0.3627	0.4209	0.1843	0.4405	0.4367	0.2326	0.1867	0.2453	0.3455
	1	494.9122	2.3451	378.7337	1.3656	1.1914	1.3549	0.5190	1.5744	1.5693	0.6876	0.5316	0.8023	1.2228
	5	503.2993	57.3636	378.2001	30.9619	26.3464	28.6807	10.2081	38.8394	37.9620	13.7355	11.1733	23.5614	34.3006
	10	532.7590	213.6679	381.2322	114.2745	97.1373	105.5232	37.3810	143.7064	141.0203	48.2938	43.5950	101.2758	134.1682
0.999	0.1	4969.1344	5.7404	3794.8173	3.1926	2.7530	3.1148	1.0561	3.9311	3.7796	1.4735	1.0616	1.6793	3.0110
	1	4973.9821	22.5688	3796.9397	12.1422	10.3665	11.4408	3.7689	15.1519	14.7909	5.3805	3.8051	7.1422	12.6832
	5	4995.4508	540.7746	3730.1907	281.9896	239.2546	258.5691	83.8542	353.4930	350.4758	118.9266	87.5022	245.6556	339.7473
	10	5377.6750	2152.1231	3860.4020	1142.1380	967.5422	1063.4883	321.1969	1428.4656	1422.1817	453.0490	348.1526	1126.7981	1402.4136