Two-Parameter Modified Ridge-Type M-Estimator for Linear Regression Model

Table 2

Estimated MSEs of OLS, MRE, MRE, MRT, and RTMME at n = 20 and p = 3 when there is one outlier.

k	Sigma	Rho	d = 0.2						d = 0.5						d = 0.8
			0.3	1	0.7	14.015	6.603	12.842	6.066	12.628	5.968	14.015	6.603	12.842	6.066	12.319	5.827	14.015	6.603	12.842	6.066	12.023	5.691
0.8	21.072	9.888			18.352	8.633	17.879	8.414	21.072	9.888	18.352	8.633	17.207	8.104	21.072	9.888	18.352	8.633	16.576	7.813
0.9	608.818	1.152			592.046	1.140	410.694	0.853	608.818	1.152	592.046	1.140	376.593	0.800	608.818	1.152	592.046	1.140	346.658	0.753
0.99	8184.099	14.132			5874.695	12.202	574.320	1.601	8184.099	14.132	5874.695	12.202	411.088	1.239	8184.099	14.132	5874.695	12.202	308.936	1.004
5	0.7	1.125		0.924	1.120	0.920	1.119	0.919	1.125	0.924	1.120	0.920	1.118	0.918	1.125	0.924	1.120	0.920	1.116	0.917
	0.8	1.639		1.292	1.628	1.284	1.626	1.282	1.639	1.292	1.628	1.284	1.623	1.279	1.639	1.292	1.628	1.284	1.620	1.277
	0.9	122.561		1.152	122.425	1.152	120.476	1.136	122.561	1.152	122.425	1.152	119.964	1.133	122.561	1.152	122.425	1.152	119.454	1.129
	0.99	1646.049		14.129	1622.592	14.043	1331.117	11.784	1646.049	14.129	1622.592	14.043	1266.599	11.296	1646.049	14.129	1622.592	14.043	1206.688	10.841
10	0.7	0.203		0.127	0.203	0.127	0.203	0.127	0.203	0.127	0.203	0.127	0.203	0.127	0.203	0.127	0.203	0.127	0.203	0.127
	0.8	0.306		0.190	0.306	0.190	0.306	0.190	0.306	0.190	0.306	0.190	0.305	0.190	0.306	0.190	0.306	0.190	0.305	0.190
	0.9	61.768		1.152	61.751	1.152	61.506	1.148	61.768	1.152	61.751	1.152	61.441	1.147	61.768	1.152	61.751	1.152	61.376	1.146
	0.99	828.724		14.128	825.755	14.106	784.255	13.474	828.724	14.128	825.755	14.106	773.701	13.318	828.724	14.128	825.755	14.106	763.361	13.165
0.7	1	0.7	14.015	6.603	11.526	5.464	11.120	5.279	14.015	6.603	11.526	5.464	10.558	5.022	14.015	6.603	11.526	5.464	10.044	4.787
		0.8	21.072	9.888	15.549	7.339	14.735	6.963	21.072	9.888	15.549	7.339	13.644	6.459	21.072	9.888	15.549	7.339	12.684	6.016
		0.9	608.818	1.152	592.046	1.140	269.408	0.631	608.818	1.152	592.046	1.140	230.019	0.568	608.818	1.152	592.046	1.140	198.852	0.517
		0.99	8184.099	14.132	5874.695	12.202	148.737	0.616	8184.099	14.132	5874.695	12.202	101.143	0.496	8184.099	14.132	5874.695	12.202	73.364	0.425
	5	0.7	1.125	0.924	1.114	0.914	1.112	0.912	1.125	0.924	1.114	0.914	1.108	0.910	1.125	0.924	1.114	0.914	1.105	0.907
		0.8	1.639	1.292	1.614	1.272	1.610	1.268	1.639	1.292	1.614	1.272	1.603	1.262	1.639	1.292	1.614	1.272	1.596	1.256
		0.9	122.561	1.152	122.425	1.152	117.781	1.116	122.561	1.152	122.425	1.152	116.631	1.108	122.561	1.152	122.425	1.152	115.498	1.099
		0.99	1646.049	14.129	1622.592	14.043	1035.101	9.523	1646.049	14.129	1622.592	14.043	935.995	8.750	1646.049	14.129	1622.592	14.043	850.550	8.075
	10	0.7	0.203	0.127	0.203	0.127	0.203	0.127	0.203	0.127	0.203	0.127	0.203	0.127	0.203	0.127	0.203	0.127	0.202	0.127
		0.8	0.306	0.190	0.305	0.190	0.305	0.190	0.306	0.190	0.305	0.190	0.304	0.189	0.306	0.190	0.305	0.190	0.304	0.189
		0.9	61.768	1.152	61.751	1.152	61.160	1.143	61.768	1.152	61.751	1.152	61.009	1.141	61.768	1.152	61.751	1.152	60.859	1.138
		0.99	828.724	14.128	825.755	14.106	730.360	12.676	828.724	14.128	825.755	14.106	708.525	12.351	828.724	14.128	825.755	14.106	687.663	12.040
0.9	1	0.7	14.015	6.603	10.954	5.203	10.481	4.987	14.015	6.603	10.954	5.203	9.837	4.692	14.015	6.603	10.954	5.203	9.260	4.429
		0.8	21.072	9.888	14.408	6.812	13.499	6.392	21.072	9.888	14.408	6.812	12.307	5.842	21.072	9.888	14.408	6.812	11.285	5.370
		0.9	608.818	1.152	592.046	1.140	225.122	0.560	608.818	1.152	592.046	1.140	187.451	0.499	608.818	1.152	592.046	1.140	158.695	0.452
		0.99	8184.099	14.132	5874.695	12.202	96.278	0.484	8184.099	14.132	5874.695	12.202	64.898	0.403	8184.099	14.132	5874.695	12.202	46.836	0.358
	5	0.7	1.125	0.924	1.111	0.912	1.108	0.909	1.125	0.924	1.111	0.912	1.104	0.905	1.125	0.924	1.111	0.912	1.100	0.902
		0.8	1.639	1.292	1.608	1.266	1.602	1.261	1.639	1.292	1.608	1.266	1.593	1.254	1.639	1.292	1.608	1.266	1.584	1.246
		0.9	122.561	1.152	122.425	1.152	116.468	1.106	122.561	1.152	122.425	1.152	115.018	1.095	122.561	1.152	122.425	1.152	113.596	1.085
		0.99	1646.049	14.129	1622.592	14.043	923.015	8.648	1646.049	14.129	1622.592	14.043	817.497	7.812	1646.049	14.129	1622.592	14.043	729.190	7.100
	10	0.7	0.203	0.127	0.203	0.127	0.203	0.127	0.203	0.127	0.203	0.127	0.202	0.127	0.203	0.127	0.203	0.127	0.202	0.126
		0.8	0.306	0.190	0.305	0.190	0.304	0.189	0.306	0.190	0.305	0.190	0.304	0.189	0.306	0.190	0.305	0.190	0.303	0.189
		0.9	61.768	1.152	61.751	1.152	60.988	1.140	61.768	1.152	61.751	1.152	60.795	1.137	61.768	1.152	61.751	1.152	60.603	1.134
		0.99	828.724	14.128	825.755	14.106	705.487	12.306	828.724	14.128	825.755	14.106	679.005	11.910	828.724	14.128	825.755	14.106	653.998	11.535