Mathematical Problems in Engineering

Research Article

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

Table 3

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	0.9549	0.8828	0.8548	0.8509	2.6656	1.3999	1.1103	0.9331	107.84	37.012	21.997	12.665	999.65	292.18	174.44	99.6465
k1	0.8693	0.8519	0.8418	0.8436	1.2310	0.9154	0.8361	0.7889	26.028	10.680	6.7173	3.9828	237.93	71.309	41.453	23.125
k2	0.9523	0.8826	0.8548	0.8509	2.0568	1.3588	1.1030	0.9319	3.6115	7.1387	10.337	9.6812	3.5813	5.0895	8.6072	18.578
k3	0.9358	0.8803	0.8540	0.8507	1.0675	1.0309	0.9510	0.8735	1.0959	1.2321	1.3165	1.2734	1.2386	1.4244	1.5773	1.5865
k4	0.8562	0.8546	0.8514	0.8523	0.8206	0.8137	0.8028	0.7820	2.2733	2.0529	1.9110	1.7191	3.4269	2.8376	2.5492	2.1953
k5	0.8472	0.8518	0.8428	0.8455	0.7733	0.7907	0.7871	0.7786	1.7594	1.8006	1.8092	1.6575	2.5217	2.4822	2.4258	2.1150
k6	0.9265	0.8786	0.8533	0.8504	1.9220	1.2823	1.0615	0.9157	50.296	26.348	17.401	10.869	347.89	129.09	87.706	58.169
k7	0.9138	0.8757	0.8525	0.8501	1.6614	1.2155	1.0406	0.9099	32.099	20.938	15.412	10.241	130.20	85.090	73.516	56.181
k8	0.8734	0.8713	0.8515	0.8499	0.7396	0.7860	0.7995	0.7996	0.7272	0.8704	0.9937	1.0466	0.7243	0.8834	1.1067	1.2639
k9	0.9138	0.8757	0.8525	0.8501	1.6614	1.2155	1.0406	0.9099	32.099	20.938	15.412	10.241	130.20	85.090	73.516	56.181
k10	0.8649	0.8579	0.8452	0.8463	0.8478	0.8347	0.8135	0.7891	1.8830	1.7778	1.7320	1.5487	3.2077	2.7177	2.5165	2.1731
k11	0.8877	0.8741	0.8523	0.8501	0.7745	0.8223	0.8236	0.8142	0.7823	0.9493	1.0824	1.1073	0.7624	0.9622	1.1873	1.3195
k12	0.8877	0.8741	0.8523	0.8501	0.7745	0.8223	0.8236	0.8142	0.7823	0.9493	1.0824	1.1073	0.7624	0.9622	1.1873	1.3195
k13	0.8638	0.8616	0.8473	0.8477	0.7784	0.8083	0.8048	0.7919	1.0790	1.2059	1.3122	1.2768	1.3410	1.5506	1.7112	1.6848
k14	0.8826	0.8713	0.8512	0.8497	0.7777	0.8203	0.8183	0.8060	0.8616	1.0001	1.1140	1.1297	0.9211	1.1786	1.3559	1.4254
k15	0.8720	0.8641	0.8481	0.8481	0.8174	0.8350	0.8201	0.7994	1.2754	1.3738	1.4523	1.3711	1.7723	1.8692	1.9592	1.8282
k16	0.8819	0.8711	0.8511	0.8497	0.7765	0.8187	0.8168	0.8053	0.8576	1.0025	1.1152	1.1275	0.8764	1.1505	1.3377	1.4106
k17	0.9541	0.8827	0.8548	0.8509	2.5904	1.3898	1.1076	0.9325	77.004	31.752	20.333	12.164	645.63	225.84	150.89	92.015
k18	0.8712	0.8647	0.8485	0.8484	0.9032	0.9124	0.8778	0.8364	3.4582	3.5459	3.3937	3.0611	4.7972	4.1832	3.7004	3.2521
k19	0.9138	0.8757	0.8525	0.8501	1.6614	1.2155	1.0406	0.9099	32.099	20.938	15.412	10.241	130.20	85.090	73.516	56.181
k20	0.8505	0.8527	0.8439	0.8457	0.7591	0.7794	0.7818	0.7718	1.1097	1.1628	1.2236	1.1951	1.4290	1.5587	1.6729	1.6362
k21	0.8585	0.8492	0.8417	0.8437	0.9973	0.8569	0.8146	0.7802	9.2168	5.5203	4.0567	2.8155	35.218	17.900	12.355	8.2841
k22	0.8682	0.8592	0.8457	0.8465	0.9033	0.8507	0.8213	0.7928	2.5221	2.2379	2.1291	1.8072	5.0738	4.0625	3.5840	2.9654
k23	0.8304	0.8392	0.8364	0.8401	0.8059	0.7547	0.7457	0.7367	0.9876	0.9695	0.9545	0.9300	0.9968	0.9947	0.9928	0.9895
k24	0.8472	0.8518	0.8428	0.8455	0.7733	0.7907	0.7871	0.7786	1.7594	1.8006	1.8092	1.6575	2.5217	2.4822	2.4258	2.1150
k25	0.8468	0.8567	0.8453	0.8468	0.7163	0.7262	0.7321	0.7317	0.8303	0.7338	0.6899	0.6999	0.9302	0.8593	0.7878	0.7117
k26	0.9138	0.8757	0.8525	0.8501	1.6614	1.2155	1.0406	0.9099	32.099	20.938	15.412	10.241	130.20	85.090	73.516	56.181
k27	0.8420	0.8500	0.8428	0.8457	0.7241	0.7289	0.7313	0.7299	0.8672	0.7883	0.7123	0.6877	0.9345	0.8697	0.7887	0.7053
k28	0.8594	0.8514	0.8430	0.8453	1.2180	0.9182	0.8491	0.7984	2.7039	4.2453	5.0926	4.1313	2.7904	3.9409	5.6849	9.0850
k29	0.8922	0.8705	0.8514	0.8498	0.8775	0.9007	0.8856	0.8411	1.0673	1.2712	1.4599	1.4827	1.2851	1.5285	1.7081	1.7069
k30	0.9118	0.8763	0.8531	0.8504	0.9906	0.9970	0.9487	0.8783	1.3500	1.6374	1.9184	2.0000	1.7783	2.0197	2.2378	2.2075
k31	0.9006	0.8729	0.8519	0.8499	1.0043	0.9695	0.9190	0.8627	1.6456	1.8978	2.1325	2.1540	2.3650	2.6005	2.8481	3.0435
k32	0.8715	0.8634	0.8492	0.8489	0.7780	0.8099	0.8196	0.7997	0.8501	0.9898	1.1085	1.1345	0.9601	1.1657	1.3391	1.4019
k33	0.8585	0.8605	0.8461	0.8470	0.7520	0.7704	0.7691	0.7585	0.8964	1.0191	1.1094	1.0857	0.9168	1.1263	1.2752	1.3210
k34	0.8324	0.8382	0.8360	0.8386	0.7157	0.7255	0.7291	0.7277	0.7094	0.7868	0.8553	0.8913	0.7318	0.8805	1.0127	1.0970
k35	0.8368	0.8437	0.8376	0.8407	0.7179	0.7324	0.7352	0.7323	0.7939	0.8798	0.9452	0.9614	0.8454	1.0312	1.1610	1.2224
k36	0.9452	0.8818	0.8546	0.8509	1.4715	1.2213	1.0569	0.9196	1.9811	2.4508	2.8365	3.0381	2.5345	2.6952	2.9125	2.8724
k37	0.8659	0.8637	0.8469	0.8475	0.7985	0.8075	0.7872	0.7733	1.2460	1.3208	1.3172	1.2166	1.5072	1.6244	1.6920	1.5920
k38	0.8623	0.8605	0.8468	0.8476	0.7639	0.7800	0.7779	0.7712	0.9616	1.0316	1.0915	1.0937	1.1592	1.2812	1.4030	1.4363
k39	0.8585	0.8492	0.8417	0.8437	0.9973	0.8569	0.8146	0.7802	9.2168	5.5203	4.0567	2.8155	35.218	17.900	12.355	8.2841
k40	0.8900	0.8746	0.8524	0.8502	0.7799	0.8297	0.8295	0.8175	0.8004	0.9737	1.1093	1.1313	0.7820	1.0408	1.2609	1.3682