Mathematical Problems in Engineering

Research Article

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

Table 4

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	2484.5	1187.2	560.14	290.20	4.56 × 106	406988	142161	65293	5.82 × 106	728304	230827	104187	4.03 × 1012	6.50 × 108	1.91 × 107	1.81 × 107
k1	623.13	322.36	167.38	94.013	709596	84265	37329	18426	1.04 × 106	161216	58159	27081	1.21 × 1010	8.21 × 107	7.95 × 106	2.90 × 106
k2	11.860	20.842	33.719	55.802	1.4093	8.2212	55.802	236.23	1.5371	9.3157	60.000	236.70	0.9247	1.0417	4.0636	37.127
k3	4.0221	7.4169	11.779	15.724	0.8989	0.8674	0.9478	1.5839	0.8966	0.8696	0.9896	1.7828	0.9783	0.9587	0.9285	0.8886
k4	87.613	60.920	48.109	36.011	15276	4195.7	3154.4	2437.7	13366	3812.2	2657.7	2053.6	7.94 × 106	154806	34057	24302
k5	57.755	61.642	69.330	70.516	4581.3	2589.6	3348.0	4258.0	3718.6	2124.2	2511.1	2931.8	1.86 × 106	51300	25630	26598
k6	1955.6	1102.93	544.94	287.25	2.10 × 106	346837	136164	64426	2.99 × 106	613557	221020	102789	3.71 × 1010	3.27 × 108	3.47 × 107	1.15 × 107
k7	1538.8	965.57	511.20	278.06	1.24 × 106	270365	121050	61142	1.58 × 106	444829	188775	95661	1.19 × 1010	1.68 × 108	2.36 × 107	9.83 × 106
k8	0.9061	0.8993	1.5473	4.3309	1.0003	0.9911	0.9669	0.9190	1.0014	0.9937	0.9739	0.9314	1.0048	1.0043	1.0029	0.9994
k9	1538.8	965.57	511.20	278.06	1.24 × 106	270365	121050	61142	1.58 × 106	444829	188775	95661	1.19 × 1010	1.68 × 108	2.36 × 107	9.83 × 106
k10	18.199	20.560	22.179	22.800	192.53	255.39	341.71	459.18	234.41	276.37	370.55	468.64	2847.5	1478.2	1886.0	2729.3
k11	0.9456	1.3711	3.4197	7.8951	0.9912	0.9691	0.9213	0.8927	0.9942	0.9737	0.9316	0.8955	1.0042	1.0028	0.9983	0.9885
k12	0.9456	1.3711	3.4197	7.8951	0.9912	0.9691	0.9213	0.8927	0.9942	0.9737	0.9316	0.8955	1.0042	1.0028	0.9983	0.9885
k13	8.4313	13.022	16.954	19.686	8.7769	28.326	80.893	193.38	9.0745	28.873	82.080	188.09	5.2666	13.425	50.143	184.91
k14	1.3133	2.8079	6.3984	11.313	0.9373	0.8789	0.8880	1.4225	0.9417	0.8816	0.8825	1.4163	0.9933	0.9765	0.9408	0.8874
k15	10.399	14.589	17.957	20.305	18.794	47.867	109.76	226.81	22.213	53.319	118.39	229.81	23.669	51.313	135.00	366.03
k16	1.3553	2.9418	6.5900	11.469	0.9378	0.8803	0.9016	1.5155	0.9433	0.8845	0.8986	1.5191	0.9945	0.9786	0.9428	0.8898
k17	424.67	343.84	259.36	186.67	22932	4986.7	5160.0	4252.3	26739	10917	8570.6	6064.1	4.69 × 106	704942	245716	138955
k18	278.42	268.43	237.49	180.65	30260	15073	18687	20534	21792	10679	13696	17373	9.08 × 107	222878	90696	131763
k19	1538.8	965.57	511.20	278.06	1.24 × 106	270365	121050	61142	1.58 × 106	444829	188775	95661	1.19 × 1010	1.68 × 108	2.36 × 107	9.83 × 106
k20	10.144	12.774	15.162	16.935	54.514	91.700	156.52	254.83	57.608	93.393	162.61	260.20	274.83	174.20	317.09	677.06
k21	249.14	141.19	87.928	55.812	159935	24024	13196	7371.2	183456	38184	16779	8947.9	1.71 × 109	1.10 × 107	1.20 × 106	590990
k22	19.220	21.587	23.029	23.498	218.84	284.40	369.25	478.93	276.92	314.12	406.64	495.01	4312.6	2016.3	2408.2	3366.0
k23	1.0047	1.0045	1.0040	1.0029	1.0050	1.0050	1.0050	1.0050	1.0050	1.0050	1.0050	1.0050	1.0050	1.0050	1.0050	1.0050
k24	57.755	61.642	69.330	70.516	4581.3	2589.6	3348.0	4258.0	3718.6	2124.2	2511.1	2931.8	1.86 × 107	51300	25630	26598
k25	1.0031	1.0017	0.9989	0.9934	1.0050	1.0050	1.0050	1.0049	1.0050	1.0050	1.0050	1.0049	1.0050	1.005	1.0050	1.0050
k26	1538.8	965.57	511.20	278.06	1.24 × 106	270365	121050	61142	1.58 × 106	444829	188775	95661	1.19 × 1010	1.68 × 108	2.36 × 107	9.83 × 106
k27	0.9767	0.9765	0.9757	0.9748	0.9775	0.9775	0.9775	0.9775	0.9775	0.9775	0.9775	0.9775	0.9775	0.9775	0.9775	0.9775
k28	2.5573	7.9242	15.985	21.591	0.9657	0.9350	0.9784	2.0596	0.9651	0.9305	0.9946	2.4442	0.9945	0.9867	0.9694	0.9459
k29	2.6472	4.9801	8.6735	12.628	1.0826	1.7897	5.2654	16.192	1.1215	1.8766	5.3098	17.270	0.9410	1.0137	1.6012	3.9912
k30	4.4004	8.2178	12.878	16.978	1.7009	3.5708	11.296	35.952	1.8863	4.1726	12.566	40.512	1.4182	1.7937	3.9680	12.285
k31	4.2101	7.6379	11.947	15.928	1.8907	3.1882	9.8312	30.394	1.8983	3.4303	10.533	32.178	1.5888	1.5883	2.8804	7.7587
k32	1.4188	2.4968	4.7968	7.9843	0.9282	1.0452	1.9493	5.0784	0.9319	1.0406	1.8693	5.2020	0.9538	0.9258	0.9843	1.4223
k33	4.8024	8.6833	13.081	16.755	1.6594	4.4703	13.545	40.632	1.5614	4.7022	14.323	40.156	1.0069	1.3958	3.4841	11.543
k34	0.9451	1.1956	1.8060	2.8796	0.9236	0.8739	0.9125	1.2420	0.9302	0.8811	0.9134	1.2610	0.9873	0.9620	0.9154	0.8843
k35	2.1147	3.8724	6.7394	9.8607	0.9442	1.2299	2.6995	7.1067	0.9360	1.1946	2.5929	6.7381	0.9650	0.9309	0.9576	1.3561
k36	7.4620	12.621	17.456	20.981	1.9130	3.2925	8.6942	29.084	2.3874	4.5044	11.076	35.826	3.3175	1.9366	2.9460	6.6976
k37	10.476	14.220	18.821	20.261	14.859	24.040	51.993	107.95	8.1316	111.80	50.927	105.62	8.2071	18.889	48.997	78.194
k38	9.4530	13.211	16.718	19.322	12.385	20.978	43.904	98.889	12.668	21.571	44.816	99.079	58.222	13.414	21.214	47.468
k39	249.14	141.19	87.928	55.812	159935	24024	13196	7371.2	183456	38184	16779	8947.9	1.71 × 109	1.10 × 107	1.20 × 106	590990
k40	0.9622	1.4630	3.8650	8.7911	0.9906	0.9670	0.9186	0.9041	0.9935	0.9715	0.9259	0.8920	1.0041	1.0024	0.9974	0.9863