More on the Ridge Parameter Estimators for the Gamma Ridge Regression Model: Simulation and Applications

Table 9

EMSE, when and .

Estimators
	n = 25	n = 50	n = 100	n = 200	n = 25	n = 50	n = 100	n = 200	25	50	100	200	25	50	100	200
MLE	1.19 × 106	50275	11594	4539.1	460923	37968	9900.4	4075.2	19.790	9.7643	4.4577	2.6011	5.45 × 1010	2.41 × 107	2.15 × 106	635466
k1	110877	8097.9	2843.2	1309.3	51610	6882.1	2497.9	1124.1	5.3504	3.0594	1.8118	1.3616	2.91 × 108	2.70 × 106	402580	159854
k2	1.7492	6.4316	19.637	50.191	2.2311	7.3172	18.787	39.811	5.5736	6.4880	4.1404	2.5655	1.0335	2.6542	12.962	49.377
k3	1.0877	1.7043	3.4140	7.6102	1.2640	2.2461	4.5891	9.0922	2.5476	2.7191	2.4787	2.0227	0.9456	1.0055	1.2682	2.2578
k4	2992.1	485.79	270.83	170.00	1118.1	280.60	175.32	113.59	1.1651	1.1125	1.0222	0.9889	1.63 × 106	5429.0	1843.5	1349.8
k5	730.07	241.84	373.82	559.77	186.11	98.517	155.02	235.57	1.0032	1.0380	1.0782	1.1252	262550	562.34	409.85	604.54
k6	324284	38381	11128	4484.9	165662	30748	9550.9	4028.8	16.167	9.0709	4.3593	2.5816	6.50 × 108	1.33 × 107	2.00 × 106	625376
k7	235937	32920	10611	4410.2	113074	25937	9045.8	3947.0	13.338	8.2949	4.2210	2.5476	3.82 × 108	8.75 × 106	1.72 × 106	594280
k8	0.9865	0.9647	1.0538	2.0649	0.9820	0.9634	1.0810	2.2349	0.9391	0.9696	1.0280	1.1469	1.0031	0.9995	0.9886	0.9673
k9	240058	30816	10231	4352.1	110582	24678	8999.5	3912.6	13.129	7.9135	4.1747	2.4915	3.12 × 108	8.43 × 106	1.66 × 106	589843
k10	47.659	41.831	50.734	61.908	36.449	34.185	39.956	42.426	1.3448	1.3278	1.2356	1.1729	837.22	199.07	195.08	228.12
k11	0.9728	1.0660	1.9533	6.1117	0.9686	1.0889	2.0980	6.1116	0.9979	1.1193	1.3498	1.4965	1.0013	0.9922	0.9716	0.9943
k12	0.9728	1.0660	1.9533	6.1117	0.9686	1.0889	2.0980	6.1116	0.9979	1.1193	1.3498	1.4965	1.0013	0.9922	0.9716	0.9943
k13	4.7866	9.7449	19.042	32.978	4.5145	8.6659	15.099	23.087	1.0098	1.0718	1.1196	1.1592	6.1015	11.455	26.699	58.845
k14	1.0107	1.6693	4.0829	10.401	1.0483	1.8921	4.5211	10.126	1.0241	1.1377	1.2934	1.3880	0.9713	0.9768	1.2442	2.9132
k15	8.0659	13.587	23.408	37.650	7.5736	12.241	19.137	26.422	1.1798	1.2677	1.2954	1.2905	19.300	26.954	46.915	84.014
k16	1.0065	1.6854	4.2256	10.774	1.0386	1.8799	4.6051	10.369	1.0205	1.1365	1.2987	1.3922	0.9747	0.9728	1.2114	2.8181
k17	99008	9269.5	4003.4	2330.0	53020	9979.2	4546.3	2459.1	19.078	9.2395	4.4484	2.5991	1.28 × 107	1.55 × 106	298878	160409
k18	9660.8	3385.3	3596.7	2777.0	2893.2	1669.1	2077.7	1896.3	2.4196	2.5495	2.3782	1.9628	2.23 × 106	9469.9	7038.2	15233
k19	240057	30816	10231	4352.2	110582	24677	8999.4	3912.7	13.195	7.9652	4.2292	2.5488	3.12 × 108	8.43 × 106	1.66 × 106	589844
k20	10.517	11.533	16.601	23.257	8.0725	10.006	13.583	17.761	0.9707	0.9950	0.9858	0.9814	55.089	29.932	43.861	70.989
k21	24188	2241.2	945.39	505.10	11992	1824.7	780.74	386.36	2.2314	1.6109	1.2288	1.0886	4.21 × 107	403633	79695	35132
k22	61.762	51.350	59.100	69.130	48.549	42.144	47.813	47.960	1.4940	1.4232	1.2932	1.2198	1322.2	266.47	242.12	277.40
k23	1.0041	1.0041	1.0039	1.0037	1.0041	1.0040	1.0039	1.0036	0.9532	0.9497	0.9387	0.9415	1.0041	1.0041	1.0041	1.0041
k24	733.16	246.10	371.26	557.76	184.95	100.86	155.66	236.62	1.0040	1.0390	1.0822	1.1234	269686	571.39	406.17	604.75
k25	1.0039	1.0037	1.0032	1.0024	1.0039	1.0036	1.0029	1.0020	0.9288	0.9412	0.9397	0.9432	1.0041	1.0041	1.0041	1.0041
k26	240057	30816	10231	4352.2	110582	24677	8999.4	3912.7	13.195	7.9652	4.2292	2.5488	3.12 × 108	8.43 × 106	1.66 × 106	589844
k27	0.9672	0.9671	0.9669	0.9666	0.9672	0.9671	0.9669	0.9666	0.8979	0.9049	0.9019	0.9051	0.9673	0.9673	0.9673	0.9673
k28	1.8040	5.3422	15.705	38.379	2.3066	6.8309	18.001	34.056	8.2036	4.8810	2.6595	1.7511	1.1203	1.9575	5.5450	20.636
k29	1.4525	2.5657	5.4101	11.703	1.5549	2.7643	5.5611	10.444	0.9943	1.0499	1.0877	1.1282	1.1806	1.7601	3.8901	9.9269
k30	2.4023	4.5919	9.5789	18.964	2.5738	4.8586	9.3053	15.831	1.1380	1.2855	1.3748	1.4015	2.5177	3.8006	8.9451	22.362
k31	2.3824	4.4628	9.3948	18.760	2.5153	4.6700	8.9151	15.518	1.1065	1.2239	1.2870	1.3230	2.2560	3.2904	7.3941	19.382
k32	1.0308	1.3261	2.2203	4.7364	1.0519	1.4073	2.4323	4.8172	0.9422	0.9626	0.9712	0.9882	0.9707	1.0807	1.5470	3.1596
k33	2.3735	6.1570	13.367	24.283	2.5350	6.0765	11.552	18.552	1.1258	1.2472	1.3625	1.3783	1.4391	3.9308	12.007	31.962
k34	0.9712	1.1598	1.8992	3.9573	0.9741	1.2187	2.0457	4.2423	0.9295	0.9451	0.9438	0.9451	0.9880	0.9763	1.0455	1.6458
k35	1.3223	2.9901	7.3060	15.441	1.3878	3.0498	6.5869	12.637	0.9568	0.9759	0.9860	0.9907	0.9843	1.2414	2.7364	9.0538
k36	3.1859	5.3932	10.544	20.109	3.5965	6.2815	11.210	17.737	3.4903	3.7482	3.1334	2.2979	6.9693	6.4907	12.404	25.173
k37	18.868	36.709	44.422	59.754	6.7346	33.071	26.729	44.498	1.9955	2.0829	2.0033	1.7349	6.2136	15.589	31.959	63.008
k38	5.4019	7.0314	11.819	19.505	4.4925	6.3083	10.110	15.378	1.0263	1.0600	1.1006	1.1392	14.291	8.1816	13.515	25.783
k39	24188	2241.23	945.39	505.10	11992	1824.7	780.74	386.36	2.2314	1.6109	1.2288	1.0886	4.21 × 107	403633	79695	35131
k40	0.9712	1.0833	2.1314	6.8278	0.9650	1.1265	2.2930	6.7265	1.0100	1.1479	1.4179	1.5744	1.0003	0.9887	0.9660	1.0161