Discrete Dynamics in Nature and Society

Research Article

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

Table 3

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


Model		OEL			MEL
Model


M1
n = 20	Bias	0.0808	0.0735	0.0569	0.0808	0.0735	0.0569	−0.0057	0.2179
	CP	0.8830	0.8810	0.8730	0.9060	0.9160	0.9040	0.8600	0.8460
	AL	2.2307	2.2362	2.2253	2.0756	2.1483	2.0939	2.0802	2.5970
	SD	2.8128	2.1589	2.4451	2.0376	1.5667	1.7734	0.7145	0.7947
n = 40	Bias	0.0802	0.0593	0.0465	0.0802	0.0593	0.0465	0.0005	0.2186
	CP	0.9250	0.9220	0.9200	0.9360	0.9390	0.9340	0.8720	0.8380
	AL	1.6084	1.6041	1.5973	1.3785	1.3956	1.3773	1.3959	1.7330
	SD	2.8762	2.2972	2.5172	2.0585	1.6442	1.8017	0.5858	0.6519
M2
n = 20	Bias	0.1208	0.1080	0.0809	0.1208	0.1080	0.0809	−0.0057	0.3595
	CP	0.8960	0.8810	0.8860	0.9210	0.9120	0.9140	0.8600	0.7970
	AL	2.2699	2.2669	2.2638	2.1130	2.1598	2.1265	2.0802	2.4904
	SD	2.7870	2.2731	2.4981	2.0190	1.6488	1.8112	0.7145	0.7792
n = 40	Bias	0.0904	0.0613	0.0334	0.0903	0.0613	0.0334	0.0005	0.3539
	CP	0.9360	0.9350	0.9290	0.9460	0.9460	0.9420	0.8720	0.7700
	AL	1.6311	1.6268	1.6221	1.3990	1.4102	1.3978	1.3959	1.6898
	SD	2.8535	2.3950	2.5621	2.0423	1.7142	1.8338	0.5858	0.6434
M3
n = 20	Bias	0.1151	0.1058	0.0827	0.1151	0.1058	0.0827	−0.0057	0.3179
	CP	0.8880	0.8880	0.8810	0.9080	0.9110	0.9090	0.8600	0.8320
	AL	2.2304	2.2318	2.2233	2.0755	2.1359	2.0897	2.0802	2.5149
	SD	2.7751	2.1871	2.4485	2.0104	1.5867	1.7754	0.7145	0.7820
n = 40	Bias	0.1063	0.0777	0.0574	0.1063	0.0777	0.0574	0.0005	0.3119
	CP	0.9170	0.9200	0.9200	0.9340	0.9350	0.9350	0.8720	0.7810
	AL	1.6066	1.6015	1.5959	1.3774	1.3913	1.3756	1.3959	1.6988
	SD	2.8470	2.3150	2.5181	2.0376	1.6570	1.8023	0.5858	0.6447


M1
n = 20	Bias	0.1154	0.1044	0.0841	0.1154	0.1044	0.0841	0.0054	0.3065
	CP	0.8710	0.8790	0.8700	0.8990	0.9070	0.9110	0.8670	0.8330
	AL	2.5572	2.5494	2.5434	2.3828	2.4450	2.3943	2.3166	2.9036
	SD	3.2147	2.4859	2.8035	2.3303	1.8076	2.0366	0.7536	0.8401
n = 40	Bias	0.0892	0.0646	0.0481	0.0892	0.0646	0.0481	−0.0031	0.2807
	CP	0.9140	0.9080	0.9120	0.9330	0.9250	0.9250	0.8530	0.8190
	AL	1.8363	1.8334	1.8259	1.5728	1.5948	1.5742	1.5825	2.0088
	SD	3.3133	2.6278	2.8788	2.3716	1.8811	2.0606	0.6238	0.7026
M2
n = 20	Bias	0.1713	0.1592	0.1247	0.1713	0.1592	0.1247	0.0054	0.4961
	CP	0.8980	0.8990	0.9020	0.9200	0.9230	0.9300	0.8670	0.7940
	AL	2.5756	2.5736	2.5706	2.3966	2.4466	2.4143	2.3166	2.7918
	SD	3.1657	2.6116	2.8377	2.2943	1.8953	2.0584	0.7536	0.8257
n = 40	Bias	0.0969	0.0686	0.0330	0.0969	0.0686	0.0330	−0.0031	0.4320
	CP	0.9270	0.9240	0.9300	0.9390	0.9450	0.9430	0.8530	0.7840
	AL	1.8630	1.8599	1.8546	1.5974	1.6114	1.5978	1.5825	1.9375
	SD	3.2785	2.7502	2.9305	2.3467	1.9686	2.0976	0.6238	0.6895
M3
n = 20	Bias	0.1617	0.1441	0.1180	0.1617	0.1441	0.1180	0.0054	0.4538
	CP	0.8770	0.8730	0.8710	0.9050	0.9020	0.9050	0.8670	0.8020
	AL	2.5628	2.5578	2.5536	2.3868	2.4466	2.4015	2.3166	2.8692
	SD	3.1998	2.5164	2.8125	2.3196	1.8284	2.0416	0.7536	0.8361
n = 40	Bias	0.1357	0.0998	0.0731	0.1357	0.0998	0.0731	−0.0031	0.4151
	CP	0.9130	0.9110	0.9140	0.9210	0.9290	0.9310	0.8530	0.7560
	AL	1.8326	1.8268	1.8218	1.5709	1.5859	1.5705	1.5825	1.9471
	SD	3.2652	2.6553	2.8739	2.3372	1.9007	2.0571	0.6238	0.6908


M1
n = 20	Bias	0.1535	0.1411	0.1149	0.1535	0.1411	0.1149	0.0089	0.5182
	CP	0.8710	0.8710	0.8690	0.9040	0.8960	0.9030	0.8600	0.8020
	AL	3.2116	3.1963	3.1949	2.9926	3.0561	3.0066	2.9522	3.6533
	SD	4.0680	3.1548	3.5297	2.9527	2.2992	2.5686	0.8511	0.9427
n = 40	Bias	0.1413	0.1051	0.0787	0.1413	0.1051	0.0787	−0.0012	0.4787
	CP	0.9010	0.9070	0.9060	0.9160	0.9250	0.9210	0.8540	0.7730
	AL	2.3034	2.2967	2.2896	1.9729	1.9955	1.9740	2.0039	2.5153
	SD	4.2003	3.3200	3.6119	3.0074	2.3778	2.5865	0.7018	0.7849
M2
n = 20	Bias	0.2056	0.1901	0.1481	0.2056	0.1901	0.1481	0.0089	0.7143
	CP	0.8950	0.8950	0.8990	0.9220	0.9200	0.9280	0.8600	0.7810
	AL	3.2669	3.2575	3.2575	3.0365	3.0899	3.0546	2.9522	3.5512
	SD	4.0194	3.3494	3.6082	2.9177	2.4359	2.6216	0.8511	0.9314
n = 40	Bias	0.1260	0.0965	0.0469	0.1260	0.0965	0.0469	−0.0012	0.6236
	CP	0.9330	0.9300	0.9360	0.9430	0.9400	0.9420	0.8540	0.7430
	AL	2.3612	2.3569	2.3515	2.0244	2.0398	2.0258	2.0039	2.4226
	SD	4.1723	3.5164	3.7187	2.9872	2.5179	2.6625	0.7018	0.7707
M3
n = 20	Bias	0.3124	0.2802	0.2289	0.3124	0.2802	0.2289	0.0151	1.2031
	CP	0.8730	0.8510	0.8750	0.9050	0.8830	0.9060	0.8690	0.7220
	AL	4.1418	4.0918	4.1109	3.8600	3.8767	3.8564	3.8603	4.6516
	SD	5.2121	4.1575	4.5768	3.7932	3.0398	3.3380	0.9735	1.0647
n = 40	Bias	0.1927	0.1376	0.0925	0.1927	0.1376	0.0925	−0.0012	0.6938
	CP	0.9120	0.9070	0.9170	0.9220	0.9230	0.9290	0.8540	0.6960
	AL	2.3148	2.3015	2.2977	1.9848	1.9965	1.9808	2.0039	2.4544
	SD	4.1719	3.3648	3.6280	2.9872	2.4098	2.5979	0.7018	0.7748


M1
n = 20	Bias	0.2208	0.2108	0.1787	0.2208	0.2108	0.1787	0.0151	0.8554
	CP	0.8630	0.8510	0.8630	0.8960	0.8940	0.9030	0.8690	0.7790
	AL	4.1478	4.1197	4.1233	3.8681	3.9367	3.8769	3.8603	4.7258
	SD	5.2678	4.1058	4.5875	3.8329	3.0062	3.3501	0.9735	1.0731
n = 40	Bias	0.2078	0.1658	0.1202	0.2078	0.1658	0.1202	0.0027	0.8162
	CP	0.9000	0.9060	0.9130	0.9200	0.9190	0.9250	0.8560	0.7350
	AL	2.9851	2.9730	2.9672	2.5576	2.5821	2.5593	2.6054	3.2279
	SD	5.4854	4.3172	4.6855	3.9303	3.0954	3.3581	0.8000	0.8886
M2
n = 20	Bias	0.2486	0.2389	0.1806	0.2486	0.2389	0.1806	0.0151	1.0812
	CP	0.8970	0.8810	0.8970	0.9240	0.9090	0.9220	0.8690	0.7530
	AL	4.2464	4.2105	4.2197	3.9523	3.9785	3.9607	3.8603	4.5830
	SD	5.2769	4.4156	4.7184	3.8404	3.2228	3.4385	0.9735	1.0572
n = 40	Bias	0.1611	0.1431	0.0709	0.1611	0.1431	0.0709	0.0027	0.9679
	CP	0.9300	0.9280	0.9330	0.9470	0.9360	0.9500	0.8560	0.6910
	AL	3.0743	3.0644	3.0606	2.6322	2.6501	2.6364	2.6054	3.0973
	SD	5.4867	4.6103	4.8460	3.9307	3.3039	3.4719	0.8000	0.8721
M3
n = 20	Bias	0.3124	0.2802	0.2289	0.3124	0.2802	0.2289	0.0151	1.2031
	CP	0.8730	0.8510	0.8750	0.9050	0.8830	0.9060	0.8690	0.7220
	AL	4.1418	4.0918	4.1109	3.8600	3.8767	3.8564	3.8603	4.6516
	SD	5.2121	4.1575	4.5768	3.7932	3.0398	3.3380	0.9735	1.0647
n = 40	Bias	0.2910	0.2193	0.1472	0.2910	0.2193	0.1472	0.0027	1.1758
	CP	0.9040	0.9000	0.9110	0.9200	0.9220	0.9370	0.8560	0.6100
	AL	3.0001	2.9723	2.9738	2.5739	2.5768	2.5644	2.6054	3.1358
	SD	5.4574	4.3697	4.6988	3.9111	3.1328	3.3671	0.8000	0.8764