Discrete Dynamics in Nature and Society

Research Article

Mean Empirical Likelihood Inference for Response Mean with Data Missing at Random

Table 4

Performance of the point estimators and 95% CIs for response mean in simulation 2, .


Model		OEL				MEL
Model


M1
n = 20	Bias	0.0980	0.0955	0.0804	0.0980	0.0955	0.0804	−0.0053	0.2177
	CP	0.8900	0.8810	0.8840	0.9100	0.9120	0.9150	0.8530	0.8350
	AL	2.3574	2.3634	2.3540	2.1989	2.2797	2.2196	2.1519	2.6703
	SD	2.9416	2.2382	2.5761	2.1315	1.6258	1.8695	0.7264	0.8057
n = 40	Bias	0.0606	0.0401	0.0268	0.0606	0.0401	0.0268	0.0019	0.2058
	CP	0.9230	0.9210	0.9190	0.9330	0.9370	0.9330	0.8680	0.8320
	AL	1.6724	1.6690	1.6613	1.4337	1.4539	1.4328	1.4410	1.8057
	SD	2.9763	2.3670	2.6156	2.1302	1.6942	1.8721	0.5948	0.6646
M2
n = 20	Bias	0.1227	0.1117	0.0856	0.1227	0.1117	0.0856	−0.0053	0.3586
	CP	0.8790	0.8790	0.8810	0.9020	0.9150	0.9060	0.8530	0.8150
	AL	2.3549	2.3568	2.3487	2.1940	2.2495	2.2070	2.1519	2.5743
	SD	2.8880	2.3479	2.5898	2.0923	1.7041	1.8787	0.7264	0.7921
n = 80	Bias	0.0811	0.0508	0.0243	0.0811	0.0508	0.0243	0.0019	0.3421
	CP	0.9360	0.9310	0.9350	0.9440	0.9460	0.9470	0.8680	0.7940
	AL	1.6970	1.6932	1.6876	1.4564	1.4697	1.4549	1.4410	1.7536
	SD	2.9564	2.4705	2.6611	2.1159	1.7682	1.9046	0.5948	0.6549
M3
n = 20	Bias	0.1392	0.1266	0.1050	0.1392	0.1266	0.1050	−0.0053	0.3263
	CP	0.8780	0.8790	0.8810	0.9110	0.9150	0.9160	0.8530	0.8290
	AL	2.3407	2.3431	2.3361	2.1820	2.2460	2.1991	2.1519	2.5981
	SD	2.8894	2.2687	2.5650	2.0932	1.6466	1.8604	0.7264	0.7947
n = 80	Bias	0.0918	0.0650	0.0437	0.0918	0.0650	0.0437	0.0019	0.3066
	CP	0.9290	0.9280	0.9320	0.9390	0.9460	0.9430	0.8680	0.8030
	AL	1.6750	1.6684	1.6629	1.4372	1.4516	1.4344	1.4410	1.7434
	SD	2.9589	2.3867	2.6183	2.1177	1.7083	1.8740	0.5948	0.6531


M1
n = 20	Bias	0.0991	0.0980	0.0789	0.0991	0.0980	0.0789	−0.0057	0.2874
	CP	0.8750	0.8730	0.8770	0.8970	0.9150	0.9040	0.8580	0.8330
	AL	2.6330	2.6399	2.6297	2.4551	2.5450	2.4793	2.3812	2.9765
	SD	3.3056	2.5042	2.8798	2.3965	1.8204	2.0915	0.7651	0.8508
n = 40	Bias	0.0666	0.0452	0.0262	0.0666	0.0452	0.0262	−0.0068	0.2749
	CP	0.9020	0.9150	0.9110	0.9100	0.9350	0.9290	0.8580	0.8030
	AL	1.9021	1.8972	1.8912	1.6299	1.6517	1.6316	1.6631	2.0389
	SD	3.4267	2.6980	2.9757	2.4527	1.9313	2.1300	0.6389	0.7060
M2
n = 20	Bias	0.1265	0.1133	0.0843	0.1265	0.1133	0.0843	−0.0057	0.4260
	CP	0.8950	0.9000	0.9000	0.9190	0.9270	0.9250	0.8580	0.7880
	AL	2.6613	2.6589	2.6522	2.4787	2.5309	2.4908	2.3812	2.8391
	SD	3.2597	2.6807	2.9323	2.3636	1.9468	2.1283	0.7651	0.8321
n = 40	Bias	0.0892	0.0567	0.0244	0.0892	0.0567	0.0244	−0.0068	0.4145
	CP	0.9230	0.9230	0.9190	0.9340	0.9350	0.9360	0.8580	0.7650
	AL	1.9339	1.9289	1.9246	1.6591	1.6722	1.6590	1.6631	1.9615
	SD	3.3837	2.8391	3.0365	2.4220	2.0323	2.1735	0.6389	0.6934
M3
n = 20	Bias	0.1646	0.1477	0.1237	0.1646	0.1477	0.1237	−0.0057	0.4220
	CP	0.8830	0.8730	0.8790	0.9020	0.9100	0.9070	0.8580	0.8010
	AL	2.5971	2.5984	2.5888	2.4225	2.4859	2.4314	2.3812	2.8912
	SD	3.2057	2.5433	2.8497	2.3243	1.8481	2.0690	0.7651	0.8394
n = 40	Bias	0.1091	0.0742	0.0478	0.1091	0.0742	0.0478	−0.0068	0.3910
	CP	0.9110	0.9110	0.9140	0.9270	0.9400	0.9310	0.8580	0.7740
	AL	1.9105	1.9025	1.8980	1.6388	1.6541	1.6372	1.6631	2.0048
	SD	3.3896	2.7397	2.9884	2.4262	1.9612	2.1392	0.6389	0.7006


M1
n = 20	Bias	0.1580	0.1465	0.1176	0.1580	0.1465	0.1176	−0.0058	0.4920
	CP	0.8800	0.8690	0.8780	0.9070	0.9030	0.9090	0.8560	0.8150
	AL	3.2556	3.2475	3.2379	3.0391	3.1207	3.0446	2.9838	3.7143
	SD	4.0892	3.1324	3.5685	2.9687	2.2847	2.5988	0.8565	0.9512
n = 40	Bias	0.1102	0.0826	0.0527	0.1102	0.0826	0.0527	−0.0046	0.4445
	CP	0.9180	0.9120	0.9140	0.9290	0.9270	0.9290	0.8630	0.7860
	AL	2.3729	2.3659	2.3596	2.0330	2.0576	2.0355	2.0905	2.5668
	SD	4.3127	3.3914	3.7184	3.0879	2.4292	2.6629	0.7166	0.7921
M2
n = 20	Bias	0.1523	0.1363	0.0973	0.1523	0.1363	0.0973	−0.0058	0.6213
	CP	0.8960	0.8920	0.8910	0.9210	0.9240	0.9310	0.8560	0.7880
	AL	3.3218	3.3080	3.3102	3.0877	3.1327	3.1067	2.9838	3.5378
	SD	4.0869	3.4004	3.6695	2.9676	2.4738	2.6672	0.8565	0.9286
n = 40	Bias	0.1219	0.0935	0.0426	0.1219	0.0935	0.0426	−0.0046	0.6363
	CP	0.9200	0.9200	0.9270	0.9310	0.9320	0.9320	0.8630	0.7240
	AL	2.4278	2.4195	2.4158	2.0826	2.0947	2.0818	2.0905	2.4501
	SD	4.2839	3.6014	3.8182	3.0675	2.5793	2.7343	0.7166	0.7754
M3
n = 20	Bias	0.2194	0.2007	0.1642	0.2194	0.2007	0.1642	−0.0058	0.6914
	CP	0.8700	0.8560	0.8690	0.8990	0.8900	0.9030	0.8560	0.7650
	AL	3.2062	3.1934	3.1938	2.9879	3.0523	3.0051	2.9838	3.5663
	SD	3.9945	3.1661	3.5255	2.9018	2.3080	2.5661	0.8565	0.9324
n = 40	Bias	0.1856	0.1361	0.0911	0.1856	0.1361	0.0911	−0.0046	0.6684
	CP	0.9200	0.9100	0.9180	0.9400	0.9330	0.9350	0.8630	0.7210
	AL	2.3662	2.3524	2.3495	2.0292	2.0416	2.0258	2.0905	2.5127
	SD	4.2445	3.4271	3.7071	3.0391	2.4546	2.6548	0.7166	0.7847


M1
n = 20	Bias	0.2201	0.2048	0.1692	0.2201	0.2048	0.1692	0.0042	0.8355
	CP	0.8470	0.8410	0.8440	0.8740	0.8770	0.8840	0.8400	0.7960
	AL	4.2359	4.2035	4.2082	3.9467	4.0136	3.9594	4.0717	5.0903
	SD	5.3800	4.1687	4.6843	3.9171	3.0545	3.4230	0.9983	1.1108
n = 40	Bias	0.1813	0.1383	0.0916	0.1813	0.1383	0.0916	−0.0020	0.7745
	CP	0.9200	0.9100	0.9210	0.9310	0.9340	0.9380	0.8580	0.7410
	AL	3.0360	3.0211	3.0169	2.6021	2.6244	2.6029	2.7111	3.2838
	SD	5.5618	4.3777	4.7587	3.9845	3.1381	3.4099	0.8163	0.8960
M2
n = 20	Bias	0.1914	0.1790	0.1246	0.1914	0.1790	0.1246	−0.0093	0.9730
	CP	0.9070	0.8890	0.9110	0.9280	0.9230	0.9310	0.8640	0.7640
	AL	4.2705	4.2472	4.2587	3.9727	4.0115	3.9929	3.8611	4.5488
	SD	5.3181	4.4389	4.7489	3.8693	3.2383	3.4595	0.9743	1.0532
n = 40	Bias	0.1519	0.1380	0.0644	0.1519	0.1380	0.0644	−0.0020	0.9899
	CP	0.9150	0.9160	0.9200	0.9330	0.9310	0.9390	0.8580	0.6760
	AL	3.1334	3.1201	3.1183	2.6876	2.6998	2.6878	2.7111	3.1629
	SD	5.6144	4.6827	4.9336	4.0228	3.3566	3.5354	0.8163	0.8809
M3
n = 20	Bias	0.2897	0.2575	0.2094	0.2897	0.2575	0.2094	−0.0093	1.1480
	CP	0.8500	0.8490	0.8640	0.8830	0.8710	0.8920	0.8640	0.7380
	AL	4.1124	4.0760	4.0890	3.8351	3.8662	3.8430	3.8611	4.5670
	SD	5.1916	4.1105	4.5624	3.7832	3.0098	3.3325	0.9743	1.0546
n = 40	Bias	0.2669	0.2032	0.1309	0.2669	0.2032	0.1309	−0.0020	1.1346
	CP	0.9030	0.9050	0.9190	0.9230	0.9210	0.9340	0.8580	0.6430
	AL	3.0494	3.0194	3.0215	2.6178	2.6196	2.6073	2.7111	3.1736
	SD	5.5468	4.4192	4.7703	3.9751	3.1687	3.4189	0.8163	0.8827