Mathematical Problems in Engineering

Research Article

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

Table 8

EMSE, when and .


Estimators
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	3.39 × 108	731116	102508	34590	1.84 × 107	430743	76525	31019	156.16	67.551	28.621	14.170	1.18 × 1014	9.02 × 109	2.84 × 107	4.90 × 106
k1	1.40 × 107	101986	22057	9562.9	1.35 × 106	66100	17258	8612.9	37.518	17.422	8.0940	4.4892	7.32 × 109	5.69 × 107	5.07 × 106	1.11 × 106
k2	1.1406	3.7649	19.751	76.249	1.3925	5.6779	26.015	72.717	4.1644	10.920	16.240	12.247	0.9592	1.2930	5.3532	36.012
k3	0.9580	1.0497	1.4234	2.7780	0.9827	1.2291	2.1415	5.0487	1.7065	2.0401	2.4870	2.8487	0.9702	0.9593	0.9586	1.0372
k4	288393	4251.0	1821.3	1040.1	20086	2161.9	1069.2	765.99	2.7589	2.1738	1.7358	1.4199	3.02 × 108	772774	16217	7765.6
k5	86364	1821.2	2022.7	3414.4	3394.0	638.35	831.39	1480.7	1.4453	1.5730	1.8070	2.0763	2.90 × 107	178386	2381.5	3068.9
k6	2.77 × 107	462142	96656	34122	3.88 × 106	313078	73140	30631	124.67	62.127	27.863	14.017	1.49 × 1010	2.33 × 108	2.45 × 107	4.80 × 106
k7	1.99 × 107	393087	91034	33475	2.45 × 106	255790	68533	29947	99.643	56.028	26.732	13.737	9.13 × 109	1.58 × 108	2.02 × 107	4.52 × 106
k8	1.0005	0.9903	0.9669	0.9732	0.9991	0.9871	0.9612	0.9868	0.9879	1.0721	1.1143	1.1614	1.0039	1.0032	1.0009	0.9942
k9	1.92 × 107	363061	89118	33460	2.46 × 106	237071	66391	29440	98.897	53.709	26.715	13.776	9.41 × 109	1.53 × 108	1.96 × 107	4.48 × 106
k10	177.39	100.46	125.35	175.59	112.54	91.160	109.32	137.95	2.0009	1.9531	1.8287	1.7399	9844.9	602.81	549.01	669.70
k11	0.9946	0.9793	1.0025	1.5726	0.9911	0.9718	1.0218	1.8441	1.0492	1.1261	1.1934	1.3332	1.0036	1.0015	0.9942	0.9782
k12	0.9946	0.9793	1.0025	1.5726	0.9911	0.9718	1.0218	1.8441	1.0492	1.1261	1.1934	1.3332	1.0036	1.0015	0.9942	0.9782
k13	6.2666	14.400	36.342	81.826	6.3586	14.647	34.216	65.338	1.1730	1.2361	1.3128	1.4189	9.9687	12.335	34.035	100.17
k14	0.9638	1.0418	1.6343	4.4234	0.9579	1.0997	2.0533	6.1357	1.0992	1.1611	1.2311	1.3557	0.9935	0.9741	0.9607	1.1241
k15	12.664	22.975	46.406	92.5501	13.040	23.248	44.065	74.988	1.3628	1.4597	1.5644	1.6845	38.915	39.111	76.145	164.41
k16	0.9653	1.0443	1.6851	4.7064	0.9589	1.0949	2.0965	6.4961	1.0960	1.1606	1.2348	1.3651	0.9950	0.9768	0.9609	1.1101
k17	904517	31961	10800	6680.3	362871	36724	11731	8203.6	139.14	61.273	28.028	14.127	7.62 × 107	4.71 × 106	974954	331625
k18	701190	26822	23206	19398	44452	10337	12083	12830	9.4015	10.412	10.430	8.2712	3.27 × 108	1.03 × 106	46734	77468
k19	1.92 × 107	363058	89118	33460	2.46 × 106	237070	66391	29440	98.961	53.756	26.776	13.836	9.41 × 109	1.53 × 108	1.96 × 107	4.48 × 106
k20	33.064	27.167	40.470	64.989	21.458	24.815	38.275	56.865	1.1411	1.1814	1.1907	1.1953	576.79	76.856	100.46	171.86
k21	1.91 × 106	24223	7015.7	3439.0	256078	15815	5127.6	2867.5	11.833	6.1651	3.4057	2.2712	3.77 × 109	8.64 × 106	897729	228358
k22	230.93	123.20	144.61	196.60	150.62	112.94	128.16	154.31	2.4227	2.2427	2.0169	1.8794	14206	819.47	696.51	813.54
k23	1.0041	1.0041	1.0041	1.0041	1.0041	1.0041	1.0041	1.0041	0.9949	0.9900	0.9687	0.9486	1.0041	1.0041	1.0041	1.0041
k24	106959	1844.1	2025.6	3453.9	3494.1	643.57	834.86	1475.7	1.4456	1.5777	1.8119	2.0820	2.98 × 107	192818	2385.6	3053.8
k25	1.0041	1.0041	1.0040	1.0039	1.0041	1.0041	1.0040	1.0039	0.9606	0.9506	0.9391	0.9610	1.0041	1.0041	1.0041	1.0041
k26	1.92 × 107	363058	89118	33460	2.46 × 106	237070	66391	29440	98.961	53.756	26.776	13.836	9.41 × 109	1.53 × 108	1.96 × 107	4.48 × 106
k27	0.9673	0.9673	0.9673	0.9672	0.9673	0.9673	0.9673	0.9672	0.9430	0.9343	0.9163	0.9063	0.9673	0.9673	0.9673	0.9673
k28	1.0633	1.5598	4.0106	16.139	1.1486	2.1306	6.7546	26.645	12.436	17.336	12.955	7.5426	0.9916	1.0665	1.4007	3.2204
k29	1.2364	1.8964	3.9975	10.842	1.3288	2.2183	5.0280	13.168	1.0864	1.1500	1.1983	1.2665	1.0500	1.3061	2.0993	5.2311
k30	2.3216	3.7636	8.57599	23.147	2.4431	4.5633	10.693	26.543	1.2018	1.3057	1.4310	1.6132	2.9290	2.8146	5.6189	15.288
k31	2.4016	3.6852	8.3399	22.991	2.4041	4.3431	9.9225	25.369	1.1835	1.2723	1.3524	1.5111	3.0610	2.4238	4.4474	12.465
k32	0.9862	1.1000	1.5121	3.0934	0.9989	1.1601	1.7730	3.9185	1.0027	1.0633	1.0931	1.1280	0.9707	0.9947	1.0900	1.6124
k33	1.6309	4.8683	14.837	39.910	2.0101	5.8927	17.098	38.284	1.2033	1.2889	1.4222	1.5799	1.1207	2.1208	7.0557	26.358
k34	0.9745	0.9897	1.1720	2.0862	0.9679	0.9999	1.3021	2.5691	0.9880	1.0487	1.0698	1.0972	0.9984	0.9852	0.9719	1.0631
k35	1.0389	1.8288	5.1441	16.098	1.0921	2.0772	6.0191	16.761	1.0741	1.1173	1.1355	1.1581	0.9877	1.0138	1.4185	4.0864
k36	3.5628	4.1005	8.1759	20.450	3.6225	5.6778	11.977	27.712	2.7138	3.8913	5.0528	5.5492	25.070	5.3496	7.9822	15.820
k37	7.0980	34.706	47.776	109.33	8.3073	21.601	46.875	95.911	2.8102	2.8751	3.0496	3.0529	4.5196	8.7658	69.447	93.459
k38	11.972	12.579	21.950	43.672	8.9867	11.611	21.910	39.880	1.2131	1.2645	1.3402	1.4504	128.20	14.845	19.272	36.893
k39	1.91 × 106	24223	7015.7	3439.0	256078	15815	5127.6	2867.5	11.833	6.1651	3.4057	2.2712	3.77 × 109	8.64 × 106	897729	228358
k40	0.9932	0.9769	1.0114	1.7308	0.9888	0.9688	1.0383	2.0020	1.0587	1.1334	1.2109	1.3955	1.0035	1.0007	0.9918	0.9722