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

Table 7

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	1.78 × 1013	2.52 × 108	4.99 × 106	1.08 × 106	8.45 × 1011	7.46 × 107	3.50 × 106	956068	5854.5	2152.7	860.70	403.46	4.37 × 1016	1.45 × 1014	2.46 × 109	2.20 × 108
k1	1.04 × 1010	2.27 × 107	822497	254439	8.06 × 108	7.65 × 106	643865	242101	1268.0	514.02	225.83	104.60	1.85 × 1014	2.02 × 1010	3.98 × 108	3.78 × 107
k2	0.9685	1.0421	2.7081	21.297	0.9601	1.2099	5.0828	42.885	5.4207	8.4487	15.756	41.504	0.9853	0.9676	1.0697	3.0810
k3	0.9842	0.9745	0.9569	0.9503	0.9750	0.9632	0.9516	0.9908	3.9293	5.3772	6.3611	6.9937	0.9962	0.9923	0.9844	0.9734
k4	5.93 × 108	810198	45515	22896	8.06 × 107	178688	31886	18723	42.958	27.306	20.747	14.880	6.05 × 1011	3.10 × 108	835464	200112
k5	1.54 × 108	195124	36249	59345	6.98 × 106	27221	15048	27206	12.397	14.069	17.942	22.417	1.50 × 1011	3.60 × 107	88858	49047
k6	2.05 × 1010	1.01 × 108	4.46 × 106	1.06 × 106	2.60 × 109	3.70 × 107	3.21 × 106	939987	4370.7	1959.4	836.99	398.88	2.79 × 1014	8.23 × 1010	2.35 × 109	2.10 × 108
k7	1.72 × 1010		4.04 × 106	1.04 × 106	1.73 × 109	2.89 × 107	2.92 × 106	912529	3342.2	1738.1	798.25	389.81	1.84 × 1014	5.95 × 1010	1.80 × 109	1.91 × 108
k8	1.0039	1.0033	1.0004	0.9935	1.0039	1.0030	0.9998	0.9918	0.9470	1.0104	1.5945	3.1829	1.0041	1.0041	1.0039	1.0034
k9	1.77 × 1010	8.20 × 107	3.94 × 106	1.02 × 106	1.74 × 109	2.80 × 107	2.85 × 106	904606	3337.3	1663.4	794.67	390.91	2.02 × 1014	5.89 × 1010	1.77 × 109	1.87 × 108
k10	8612.0	483.04	478.06	775.01	1890.7	450.57	513.78	776.01	9.0530	9.3386	9.0839	8.9543	616179	7983.9	2422.3	2960.9
k11	1.0035	1.0016	0.9934	0.9766	1.0034	1.0008	0.9917	0.9729	1.0035	1.5861	3.0913	4.9441	1.0041	1.0039	1.0034	1.0019
k12	1.0035	1.0016	0.9934	0.9766	1.0034	1.0008	0.9917	0.9729	1.0035	1.5861	3.0913	4.9441	1.0041	1.0039	1.0034	1.0019
k13	12.257	11.423	35.965	131.52	8.9936	13.979	44.912	148.98	4.1579	5.5758	6.5139	7.1137	50.906	11.506	22.000	77.783
k14	0.9967	0.9825	0.9580	0.9758	0.9930	0.9759	0.9545	1.0175	1.6391	3.0236	4.6118	5.8777	1.0031	0.9993	0.9897	0.9725
k15	31.547	26.701	60.311	173.24	26.224	34.028	78.400	203.46	5.2301	6.4145	7.0582	7.4980	201.66	53.938	82.405	208.88
k16	0.9971	0.9833	0.9586	0.9821	0.9939	0.9772	0.9558	1.0290	1.5921	2.9922	4.6237	5.9034	1.0032	0.9999	0.9911	0.9740
k17	3.19 × 107	341291	37920	18495	1.21 × 107	260523	40855	24937	2115.3	1141.3	625.30	341.05	1.55 × 109	4.00 × 107	5.22 × 106	820896
k18	1.20 × 109	3.44 × 106	535659	444892	1.04 × 108	543210	265860	290273	165.56	187.44	208.45	178.50		4.55 × 108		1.24 × 106
k19	1.77 × 1010	8.20 × 107	3.94 × 106	1.02 × 106	1.74 × 109	2.80 × 107	2.85 × 106	904607	3337.5	1663.4	794.70	390.96	2.02 × 1014	5.89 × 1010	1.77 × 109	1.87 × 108
k20	1480.6	106.87	124.28	215.39	306.99	98.484	143.64	250.25	4.4039	5.3021	5.8812	6.2746	38329	550.19	298.12	486.93
k21	3.94 × 109	5399067	213503	84638	2.09 × 108	1.76 × 106	177116	78840	346.70	149.88	72.244	38.708	5.47 × 1013	6.36 × 109	5.21 × 107	6.97 × 106
k22	10490	589.00	546.15	867.83	2483.3	551.77	595.77	864.07	10.753	10.560	9.8703	9.5172	943534	12961	3128.9	3792.6
k23	1.0041	1.0041	1.0041	1.0041	1.0041	1.0041	1.0041	1.0041	1.0040	1.0039	1.0033	1.0024	1.0041	1.0041	1.0041	1.0041
k24	1.56 × 108	224728	36101	59666	7.51 × 106	27577	14987	27385	12.465	14.288	17.889	22.364	1.43 × 1011	3.90 × 107	87527	49178
k25	1.0041	1.0041	1.0041	1.0041	1.0041	1.0041	1.0041	1.0041	1.0030	1.0022	1.0002	0.9967	1.0041	1.0041	1.0041	1.0041
k26	1.77 × 1010	8.20 × 107	3.94 × 106	1.02 × 106	1.74 × 109	2.80 × 107	2.85 × 106	904607	3337.5	1663.4	794.70	390.96	2.02 × 1014	5.89 × 1010	1.77 × 109	1.87 × 108
k27	0.9673	0.9673	0.9673	0.9673	0.9673	0.9673	0.9673	0.9673	0.9668	0.9665	0.9659	0.9648	0.9673	0.9673	0.9673	0.9673
k28	0.9951	0.9910	0.9917	1.0288	0.9904	0.9884	0.9970	1.1160	4.0927	6.6037	8.9366	15.018	0.9990	0.9964	0.9922	0.9934
k29	1.0107	1.0866	1.3209	2.5262	1.0283	1.1498	1.6009	3.7065	2.1682	3.2864	4.5025	5.5491	0.9919	1.0151	1.0780	1.4039
k30	2.6626	1.7358	2.5028	6.1325	2.0745	2.0259	3.5581	9.7830	3.2311	4.7044	5.8355	6.6540	5.1585	1.7755	1.9441	3.4529
k31	2.8836	1.6910	2.3432	5.9390	2.2116	1.9080	3.1633	8.9890	3.1002	4.5298	5.6648	6.5095	5.6065	1.5372	1.5666	2.6659
k32	0.9812	0.9827	0.9948	1.1395	0.9776	0.9845	1.0229	1.3034	1.3036	1.8415	2.7228	3.7354	0.9884	0.9840	0.9805	0.9997
k33	1.0438	1.4413	3.9994	14.372	1.0732	1.7906	5.6668	20.733	3.4934	5.0094	6.1043	6.8142	0.9889	1.0885	1.6135	4.8286
k34	0.9984	0.9853	0.9618	0.9793	0.9952	0.9792	0.9591	1.0139	1.0726	1.4308	2.0061	2.7768	1.0033	0.9999	0.9909	0.9722
k35	0.9879	0.9981	1.2822	3.0494	0.9807	1.0123	1.4609	3.9277	2.1249	3.3359	4.5534	5.5687	1.0009	0.9900	0.9763	1.0791
k36	14.632	2.0724	2.1233	3.5756	7.0221	2.6376	3.4018	6.8472	5.0044	6.5656	7.5279	8.3898	240.10	7.0247	2.9179	3.2250
k37	4.5811	10.575	36.664	133.67	3.9710	32.159	45.503	112.06	6.6847	8.1004	9.6153	10.636	1.7543	7.4449	147.56	70.406
k38	283.58	24.919	31.084	63.576	82.410	22.596	35.284	75.839	4.7330	5.9457	6.7551	7.2816	8382.0	85.319	26.256	38.644
k39	3.94 × 109	5.40 × 106	213503	84638	2.09 × 108		177116	78840	346.70	149.88	72.244	38.708	5.47 × 1013	6.36 × 109	5.21 × 107	6.97 × 106
k40	1.0035	1.0012	0.9922	0.9739	1.0032	1.0002	0.9900	0.9700	1.0286	1.7017	3.2948	5.1341	1.0041	1.0039	1.0032	1.0013