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

Table 17

Estimated MSE for n = 50, , and 30% outlier in the y-direction.

Correlation (δ^2)	Error variance (σ2)	OLS	M	RE	MRE	M1	TRME1	MTPM1	MTPM2	MTPM3	TRME2	MTPM4	MTPM5	MTPM6
0.85	0.1	2.8034	0.0418	0.6265	0.0301	0.0296	0.0295	0.0278	0.0279	0.0296	0.0284	0.0278	0.0279	0.0279
	1	2.8161	0.0769	0.6433	0.0447	0.0442	0.0436	0.0409	0.0413	0.0442	0.0377	0.0410	0.0411	0.0413
	5	3.1386	1.0538	0.8365	0.4012	0.3874	0.3254	0.2883	0.3042	0.3662	0.2372	0.2895	0.2952	0.3015
	10	4.1862	3.7763	1.3657	1.3162	1.2622	0.9793	0.8468	0.9418	1.1957	0.7012	0.8548	0.8891	0.9234
0.95	0.1	8.2824	0.0457	1.8604	0.0205	0.0191	0.0104	0.0083	0.0085	0.0124	0.0090	0.0083	0.0083	0.0084
	1	8.3198	0.1265	1.8804	0.0393	0.0357	0.0123	0.0074	0.0088	0.0242	0.0111	0.0074	0.0077	0.0084
	5	9.4177	2.9551	2.4566	0.9021	0.8366	0.4332	0.3113	0.5347	0.7875	0.4501	0.3170	0.3876	0.4582
	10	12.7200	11.1474	4.1154	3.4953	3.2611	1.8381	1.3945	2.5522	3.0008	1.8856	1.4409	1.8891	2.1855
0.99	0.1	42.1446	0.2038	8.7628	0.0938	0.0901	0.0757	0.0665	0.0886	0.0802	0.0836	0.0666	0.0721	0.0783
	1	42.2714	0.6839	8.9779	0.2669	0.2526	0.1863	0.1555	0.2511	0.2103	0.2115	0.1562	0.1855	0.2105
	5	47.4247	15.4249	12.0844	5.1698	4.8172	2.9603	2.2944	4.5383	3.3348	3.3375	2.3533	3.7645	4.0758
	10	65.1868	58.1920	21.0159	18.9935	17.7031	10.4142	7.9401	15.6632	11.4621	11.6153	8.3931	14.5739	14.8844
0.999	0.1	428.4407	1.6629	94.3298	0.6042	0.5652	0.3815	0.3048	0.4817	0.3127	0.3931	0.3058	0.4654	0.4918
	1	430.4556	6.4901	94.8235	2.1981	2.0435	1.2675	0.9711	1.5786	1.1062	1.2889	0.9778	1.7135	1.7367
	5	483.3848	154.7984	122.9701	50.4991	46.7159	27.1745	20.1056	29.6981	24.2687	27.0737	20.8408	38.9822	35.5692
	10	657.2009	589.6618	211.8361	190.5493	176.2327	100.3782	74.6610	106.6794	92.7202	100.7135	79.9923	143.9978	128.5776