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

Table 4

Estimated MSE for n = 20, , and 20% 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	11.8124	0.0703	5.181	0.0271	0.0258	0.0183	0.0109	0.0127	0.0293	0.0102	0.0110	0.0116	0.0129
	1	11.8312	0.2131	5.1956	0.0684	0.0648	0.0495	0.0203	0.0359	0.0806	0.0247	0.0216	0.0271	0.0368
	5	12.3381	4.4321	5.5722	1.6831	1.6024	1.3815	0.9410	1.5166	1.8005	0.9368	1.0517	1.2858	1.4946
	10	14.1711	11.3115	6.85	4.6942	4.3209	3.4207	2.6380	4.1682	5.2327	2.4187	2.8576	3.4128	3.9952
0.95	0.1	31.422	0.1506	12.8667	0.0488	0.0459	0.0330	0.0095	0.0254	0.0592	0.0127	0.0099	0.0141	0.0247
	1	31.5119	0.5661	12.9202	0.1919	0.1813	0.1525	0.0536	0.1545	0.2046	0.0728	0.0593	0.1021	0.1516
	5	33.0406	12.452	14.139	4.9587	4.6676	4.054	2.4146	4.979	4.6419	2.5501	2.9027	4.1804	4.6898
	10	39.2961	32.8009	18.3596	13.6878	12.5347	9.8595	6.7084	14.1981	14.2217	6.7705	7.8309	11.1966	13.0773
0.99	0.1	140.3318	0.7587	55.4464	0.3901	0.3693	0.3591	0.2165	0.3966	0.2790	0.2614	0.2223	0.3210	0.3728
	1	140.619	2.7976	55.5895	1.2968	1.2261	1.1633	0.6398	1.2710	0.9187	0.7727	0.6750	1.0989	1.2139
	5	149.5943	61.198	63.6205	26.3927	24.7399	21.9077	12.547	24.2947	19.807	13.8506	14.862	24.7173	23.900
	10	178.399	158.4206	81.7183	69.2094	63.4528	51.7558	32.143	70.2289	62.6102	34.6014	37.8464	64.5082	67.7464
0.999	0.1	1315.525	6.6983	512.4102	3.0299	2.831	2.6747	1.2864	2.5462	1.8925	1.6494	1.3083	2.6109	2.8092
	1	1318.783	26.1026	518.4871	11.4704	10.7198	10.2012	4.6638	8.9297	7.1542	6.009	4.8315	10.6363	10.1794
	5	1387.456	565.0867	597.5064	243.5939	226.9272	205.5404	96.7687	181.1837	165.0595	119.0271	109.1384	236.7054	197.67
	10	1720.931	1556.154	800.0413	678.0977	620.283	492.9333	269.8147	619.7776	591.5999	319.3605	307.8377	675.9897	642.3477