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

Table 1

EMSE, when and .

Estimators
	n = 25	n = 50	n = 100	n = 200	n = 25	n = 50	n = 100	n = 200	n = 25	n = 50	n = 100	n = 200	n = 25	n = 50	n = 100	n = 200
MLE	31.518	12.810	7.4891	5.0940	548.85	170.95	102.36	63.431	33123	8553.20	4820.8	2759.1	344865	72496	38657	23602
k1	10.170	5.2528	3.5534	2.8790	159.30	51.847	34.238	22.884	7539.3	2237.5	1289.9	774.09	78440	16751	8776.3	5489.5
k2	5.4285	7.5505	6.3063	4.8588	8.9885	14.153	21.989	28.889	15.716	49.046	81.527	106.43	12.219	50.420	105.49	144.81
k3	1.7094	1.9041	2.0078	2.0734	3.9179	5.5824	6.7977	7.5811	1.0586	2.3778	6.5160	15.929	0.8136	1.4764	3.8880	11.249
k4	3.6183	3.1069	2.5990	2.3475	19.991	16.415	15.861	14.039	271.48	212.99	188.54	160.47	452.73	332.11	295.10	261.35
k5	3.0608	3.3286	3.1048	2.9326	15.714	15.972	16.598	15.655	202.25	211.74	219.85	205.41	316.92	315.74	327.51	301.96
k6	24.397	11.834	7.1203	4.9531	332.61	142.29	90.608	58.847	13961	5940.3	3753.2	2354.4	112994	31125	19008	13770
k7	19.404	10.662	6.7599	4.8331	231.14	118.37	82.067	55.841	7542.7	4384.4	3169.1	2145.0	31889	18091	14760	12481
k8	0.8381	1.1817	1.4429	1.5758	0.7614	1.1258	2.4546	4.4338	0.9304	0.8474	0.8157	1.4046	0.9678	0.9204	0.8576	0.8937
k9	19.404	10.662	6.7599	4.8331	231.14	118.37	82.067	55.841	7542.7	4384.4	3169.1	2145.0	31889	18091	14760	12481
k10	1.9584	2.0052	1.9992	2.0049	8.1281	8.2988	8.9660	9.0530	61.506	69.778	80.927	86.761	113.89	119.01	137.42	147.20
k11	0.9781	1.3095	1.5152	1.6283	0.8790	1.6943	3.3517	5.2258	0.8941	0.8313	1.0832	2.8092	0.9492	0.8946	0.9381	1.2347
k12	0.9781	1.3095	1.5152	1.6283	0.8790	1.6943	3.3517	5.2258	0.8941	0.8313	1.0832	2.8092	0.9492	0.8946	0.9381	1.2347
k13	1.4927	1.6567	1.7694	1.8468	5.0254	6.5029	7.4951	8.0930	13.277	29.998	50.139	67.298	13.480	33.652	64.079	92.902
k14	1.1544	1.4148	1.5697	1.6589	1.3170	2.8816	4.7514	6.2700	0.7242	0.9163	2.4539	8.0469	0.7755	0.7500	1.3325	4.3198
k15	1.5798	1.7303	1.8302	1.8951	5.6588	6.8508	7.7430	8.2589	21.044	37.398	56.000	70.673	29.172	51.381	80.742	104.54
k16	1.1544	1.4155	1.5685	1.6579	1.3061	2.8789	4.7396	6.2587	0.7443	0.9240	2.4053	7.8554	0.8099	0.7658	1.2363	3.7984
k17	21.280	10.884	6.9574	4.9549	175.91	82.765	67.232	50.421	1294.3	760.59	765.90	773.13	9014.9	3598.4	3429.7	3832.0
k18	6.4513	6.0532	4.7174	3.9051	35.349	33.690	31.308	27.379	508.41	495.32	459.50	418.79	776.70	648.43	551.30	486.36
k19	19.404	10.662	6.7599	4.8331	231.14	118.37	82.067	55.841	7542.7	4384.4	3169.1	2145.0	31889	18091	14760	12481
k20	1.5295	1.6401	1.7122	1.7728	5.7026	6.6023	7.4225	7.8553	30.730	46.300	61.252	71.504	39.747	63.170	89.499	109.96
k21	6.3796	4.0323	3.0536	2.6216	70.837	31.627	24.547	18.511	1866.2	892.45	593.10	406.04	7840.6	3087.7	1930.3	1359.5
k22	2.0736	2.0631	2.0805	2.0668	9.2105	8.7322	9.3415	9.3922	77.528	77.556	87.922	91.956	187.27	160.57	171.82	172.20
k23	0.9845	0.9616	0.9411	0.9083	0.9973	0.9959	0.9946	0.9924	0.9981	0.9981	0.9980	0.9980	0.9981	0.9981	0.9981	0.9981
k24	3.0608	3.3286	3.1048	2.9326	15.714	15.972	16.598	15.655	202.25	211.74	219.85	205.41	316.92	315.74	327.51	301.96
k25	0.8978	0.8163	0.7326	0.6863	0.9852	0.9712	0.9491	0.9105	0.9976	0.9971	0.9962	0.9947	0.9979	0.9977	0.9975	0.9970
k26	19.404	10.662	6.7599	4.8331	231.14	118.37	82.067	55.841	7542.7	4384.4	3169.1	2145.0	31889	18091	14760	12482
k27	0.9450	0.9066	0.8225	0.7301	0.9907	0.9849	0.9707	0.9441	0.9978	0.9975	0.9970	0.9959	0.9980	0.9978	0.9976	0.9970
k28	1.8820	2.6039	2.9473	2.8756	3.2806	6.3674	8.4333	10.022	0.8087	1.4137	8.2826	35.071	0.8264	0.9878	4.1271	25.920
k29	1.2804	1.5036	1.6828	1.8216	2.9820	4.3820	5.8833	6.9047	3.2381	8.5723	20.480	34.438	3.0232	9.3517	23.158	46.306
k30	1.5230	1.8010	2.0139	2.2002	4.0589	5.8290	7.3120	8.2117	5.3798	13.806	31.542	51.372	6.6544	17.656	41.363	73.968
k31	1.4545	1.6746	1.8352	1.9814	4.0824	5.4796	6.8619	7.8211	8.5528	17.097	33.829	51.328	11.311	29.114	59.228	89.860
k32	1.0822	1.2810	1.4596	1.5940	1.9239	3.0664	4.5433	5.7466	1.3220	3.5431	9.6730	18.9740	1.0950	3.0748	8.4363	21.091
k33	1.3042	1.4971	1.6165	1.6809	2.7613	4.4346	5.7563	6.7209	3.1648	7.1861	14.329	25.281	1.8519	4.2890	8.7828	14.553
k34	0.7238	0.8407	0.9796	1.1076	0.7444	1.0084	1.4818	2.1231	0.7103	0.7811	1.1566	2.0741	0.7619	0.7468	0.9862	1.7112
k35	0.9723	1.1551	1.3009	1.4001	1.3663	2.2732	3.3058	4.3108	0.9621	1.8566	3.9397	8.0267	0.8211	1.2789	2.6533	5.5979
k36	2.4229	3.1027	3.3392	3.3923	5.9529	7.6365	9.1346	10.135	6.0246	15.667	36.925	61.218	7.6335	17.717	43.094	80.512
k37	1.5763	1.6862	1.7868	1.7900	4.0750	5.7870	6.8136	7.5683	8.8063	16.152	25.972	42.241	8.6223	15.252	27.478	44.308
k38	1.6404	1.7882	1.8843	1.9535	5.3138	6.5928	7.5043	8.0776	12.259	23.617	39.778	56.814	11.987	24.351	45.227	72.180
k39	6.3796	4.0323	3.0536	2.6216	70.837	31.627	24.547	18.511	1866.2	892.45	593.10	406.04	7840.6	3087.7	1930.3	1359.5
k40	1.0026	1.3403	1.5494	1.6593	0.9099	1.8440	3.5886	5.4674	0.8782	0.8330	1.1749	3.3760	0.9331	0.8662	0.9295	1.3857