An Improved Estimation for Heterogeneous Datasets with Lower Detection Limits regarding Environmental Health

Table 1

The amounts of AREs and MSEs for the model parameters using different estimation methods.

n	CR	Average relative estimates (AREs)					Mean square error (MSEs)
		20	MLE	1.3192	1.1499	1.2417	1.2040	1.1795	0.0407	0.0559	0.0324	0.0608	0.0216
EM	1.3149		1.1461	1.2377	1.2001	1.1757	0.0397	0.0538	0.0314	0.0588	0.0210
SELF(LA)	1.3172		1.1395	1.2355	1.1957	1.1725	0.0400	0.0508	0.0304	0.0571	0.0212
ELF(LA)	1.2852		1.1064	1.2028	1.1625	1.1408	0.0341	0.0378	0.0241	0.0453	0.0181
SELF(MCMC)	1.3078		1.1208	1.2213	1.1791	1.1577	0.0305	0.0505	0.0272	0.0510	0.0162
ELF(MCMC)	1.2674		1.1006	1.1909	1.1536	1.1307	0.0241	0.0371	0.0202	0.0378	0.0128
50	MLE	1.1898	1.0882	1.1456	1.1246	1.0949	0.0198	0.0279	0.0165	0.0345	0.0103
	EM	1.1846	1.0728	1.1353	1.1116	1.0837	0.0191	0.0240	0.0149	0.0311	0.0099
	SELF(LA)	1.1848	1.0718	1.1348	1.1109	1.0831	0.0190	0.0237	0.0148	0.0309	0.0099
	ELF(LA)	1.1602	1.0519	1.1125	1.0897	1.0621	0.0161	0.0190	0.0121	0.0254	0.0084
	SELF(MCMC)	1.1708	1.0545	1.1191	1.0943	1.0675	0.0121	0.0202	0.0111	0.0234	0.0063
	ELF(MCMC)	1.1438	1.0381	1.0973	1.0750	1.0477	0.0096	0.0161	0.0089	0.0186	0.0050
100	MLE	1.1035	1.0498	1.0829	1.0737	1.0401	0.0114	0.0177	0.0104	0.0253	0.0058
	EM	1.1026	1.0490	1.0821	1.0729	1.0393	0.0112	0.0173	0.0101	0.0248	0.0057
	SELF(LA)	1.1014	1.0462	1.0800	1.0704	1.0371	0.0111	0.0169	0.0099	0.0243	0.0056
	ELF(LA)	1.0764	1.0257	1.0572	1.0486	1.0156	0.0094	0.0138	0.0082	0.0201	0.0048
	SELF(MCMC)	1.0958	1.0376	1.0729	1.0625	1.0299	0.0064	0.0168	0.0082	0.0201	0.0033
	ELF(MCMC)	1.0728	1.0244	1.0547	1.0467	1.0135	0.0051	0.0135	0.0066	0.0161	0.0026
200	MLE	1.0387	1.0235	1.0371	1.0374	1.0305	0.0058	0.0087	0.0053	0.0140	0.0028
	EM	1.0363	1.0211	1.0347	1.0350	1.0281	0.0056	0.0084	0.0052	0.0135	0.0028
	SELF(LA)	1.0294	1.0178	1.0295	1.0307	1.0234	0.0055	0.0080	0.0050	0.0131	0.0027
	ELF(LA)	1.0206	1.0102	1.0213	1.0227	1.0154	0.0050	0.0072	0.0045	0.0118	0.0025
	SELF(MCMC)	1.0266	1.0123	1.0254	1.0258	1.0189	0.0026	0.0080	0.0039	0.0102	0.0013
	ELF(MCMC)	1.0130	1.0023	1.0135	1.0148	1.0076	0.0022	0.0070	0.0032	0.0084	0.0011