Mathematical Problems in Engineering

Research Article

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

Table 2

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	1.6449	1.0514	0.9101	0.8198	15.818	5.8671	3.7960	2.4684	839.50	266.74	160.63	91.329	7766.8	2107.5	1231.2	793.54
k1	0.9918	0.8271	0.7921	0.7586	4.7601	2.1644	1.6246	1.2703	202.72	74.041	44.047	26.123	1746.4	495.11	302.34	191.61
k2	1.5113	1.0427	0.9087	0.8195	3.7859	4.1074	3.4001	2.3965	6.0020	10.410	15.949	24.755	7.0587	10.931	15.824	18.927
k3	1.0822	0.9439	0.8716	0.8057	1.0516	1.1119	1.1645	1.1065	2.2968	3.2230	3.9134	4.2995	2.3841	3.8294	5.2280	6.1676
k4	0.8310	0.7889	0.7794	0.7598	1.3382	1.2006	1.1701	1.0630	11.963	10.189	9.3634	8.3526	20.805	14.991	14.059	12.160
k5	0.7916	0.7962	0.7951	0.7693	1.0944	1.1100	1.1555	1.0956	9.2319	9.6573	9.6389	8.9486	14.811	13.617	14.110	12.496
k6	1.4308	1.0214	0.8984	0.8155	10.002	4.9710	3.4190	2.3262	383.99	188.52	125.60	78.039	2562.4	915.57	623.21	466.45
k7	1.3112	0.9941	0.8904	0.8131	7.6767	4.3662	3.2092	2.2605	229.87	145.19	108.81	72.442	883.87	575.48	502.32	435.47
k8	0.7290	0.7674	0.7885	0.7705	0.6850	0.7413	0.8104	0.8205	0.7771	1.1840	2.1278	3.1872	0.8133	0.9298	1.5768	2.8596
k9	1.3112	0.9941	0.8904	0.8131	7.6767	4.3662	3.2092	2.2605	229.87	145.19	108.81	72.442	883.87	575.48	502.32	435.47
k10	0.8165	0.7924	0.7859	0.7602	1.1011	1.0277	1.0541	0.9889	6.1890	5.9641	6.2224	5.9743	12.455	10.153	10.652	9.9032
k11	0.7617	0.7953	0.8031	0.7779	0.7098	0.7772	0.8496	0.8503	0.9171	1.6140	2.5916	3.5083	0.8567	1.1882	2.0361	3.3048
k12	0.7617	0.7953	0.8031	0.7779	0.7098	0.7772	0.8496	0.8503	0.9171	1.6140	2.5916	3.5083	0.8567	1.1882	2.0361	3.3048
k13	0.7697	0.7830	0.7874	0.7646	0.8138	0.8606	0.9374	0.9202	3.2412	4.0169	4.6213	4.8938	4.3810	5.7584	6.8395	7.3958
k14	0.7633	0.7922	0.7985	0.7732	0.7291	0.7879	0.8649	0.8600	1.2918	2.3591	3.3378	3.9483	1.0410	2.2866	3.9287	5.3398
k15	0.7970	0.7989	0.7958	0.7686	0.8927	0.9213	0.9872	0.9536	3.7761	4.3720	4.9406	5.1260	5.7279	6.5916	7.6175	7.9520
k16	0.7644	0.7917	0.7977	0.7728	0.7312	0.7904	0.8639	0.8584	1.2446	2.3183	3.2999	3.9322	0.9539	2.0689	3.6618	5.1289
k17	1.6148	1.0474	0.9092	0.8196	13.409	5.4821	3.6842	2.4397	315.28	153.12	114.33	75.506	2193.8	930.96	739.46	586.74
k18	0.9474	0.8900	0.8465	0.7951	1.9069	1.8750	1.7672	1.5381	20.668	20.645	19.277	17.635	31.502	24.510	22.335	19.813
k19	1.3112	0.9941	0.8904	0.8131	7.6767	4.3662	3.2092	2.2605	229.87	145.19	108.81	72.442	883.87	575.48	502.32	435.47
k20	0.7595	0.7614	0.7661	0.7500	0.8268	0.8417	0.9001	0.8813	3.5923	4.0980	4.5816	4.7598	5.2953	6.1592	7.0998	7.5188
k21	0.8953	0.7977	0.7784	0.7521	2.7565	1.6349	1.3909	1.1655	62.850	34.208	23.441	16.448	227.33	110.30	80.798	58.517
k22	0.8293	0.7991	0.7914	0.7632	1.2548	1.0962	1.1077	1.0253	8.1159	7.1520	7.1420	6.6769	20.442	13.987	13.707	12.113
k23	0.7717	0.7337	0.7300	0.7236	0.9531	0.8910	0.8478	0.7933	0.9971	0.9955	0.9940	0.9914	0.9980	0.9978	0.9976	0.9973
k24	0.7916	0.7962	0.7951	0.7693	1.0944	1.1100	1.1555	1.0956	9.2319	9.6573	9.6389	8.9486	14.811	13.617	14.110	12.496
k25	0.7115	0.7157	0.7261	0.7220	0.7305	0.6804	0.6864	0.7041	0.9725	0.9462	0.9085	0.8456	0.9903	0.9806	0.9667	0.9415
k26	1.3112	0.9941	0.8904	0.8131	7.6767	4.3662	3.2092	2.2605	229.87	145.19	108.81	72.442	883.87	575.48	502.32	435.47
k27	0.7220	0.7199	0.7242	0.7200	0.7789	0.7150	0.6851	0.6933	0.9807	0.9667	0.9376	0.8841	0.9910	0.9826	0.9671	0.9375
k28	0.9439	0.8189	0.8013	0.7682	2.0468	1.9116	1.6758	1.3429	3.0898	4.8808	6.8339	8.6147	3.0953	6.0099	8.7382	10.3306
k29	0.8355	0.8248	0.8185	0.7833	0.8635	0.9318	1.0436	1.0525	2.2531	3.1174	3.9790	4.4368	2.8681	4.2335	5.6736	6.5839
k30	0.9214	0.8863	0.8536	0.8010	1.0178	1.1358	1.3009	1.2974	2.9890	3.9629	4.9115	5.3960	4.2742	5.6862	7.3151	8.0524
k31	0.8763	0.8526	0.8308	0.7900	1.0671	1.0933	1.2267	1.2125	3.4359	4.2184	5.1730	5.5810	5.6217	6.8009	8.5821	9.1210
k32	0.7687	0.7757	0.7866	0.7660	0.7513	0.7944	0.8623	0.8759	1.5039	2.3024	3.1190	3.6632	1.6318	2.7930	4.1251	5.2877
k33	0.7461	0.7600	0.7693	0.7498	0.7464	0.7924	0.8375	0.8226	1.8457	2.7901	3.4857	3.9693	1.4777	2.5819	3.6721	4.6107
k34	0.7109	0.7167	0.7227	0.7192	0.6618	0.6917	0.7199	0.7284	0.8371	1.1831	1.6573	2.1422	0.7922	1.1968	1.8269	2.5976
k35	0.7093	0.7186	0.7282	0.7218	0.6843	0.7178	0.7509	0.7516	1.3371	2.0333	2.6862	3.1844	1.1805	2.1033	3.1071	4.0502
k36	1.2795	1.0055	0.8985	0.8168	1.7759	1.9950	2.0890	1.8647	3.8818	4.9126	5.9130	6.5644	5.5138	6.7097	8.4213	9.1288
k37	0.7819	0.7867	0.7819	0.7569	0.8881	0.9062	0.9194	0.8710	3.2118	3.9296	4.4597	4.6882	3.4649	4.9875	6.1993	6.7579
k38	0.7875	0.7926	0.7932	0.7682	0.8194	0.8412	0.9032	0.8847	2.7892	3.5214	4.0819	4.4022	3.5629	4.7495	5.8802	6.5770
k39	0.8953	0.7977	0.7784	0.7521	2.7565	1.6349	1.3909	1.1655	62.850	34.208	23.441	16.448	227.33	110.30	80.798	58.517
k40	0.7652	0.8030	0.8087	0.7804	0.7149	0.7901	0.8661	0.8646	0.9309	1.7239	2.7875	3.6601	0.7984	1.2881	2.4271	3.9616