Table I.

Simulation results for ${\beta }_1$ under (M2).

$n$	${\beta }_2$	${\gamma }_1$	Lin			Buzkova			Liang (extension)			Weighted-Liang (extension)				Sun			Weighted-Sun (extension)
			Bias	ESE	MSE	Bias	ESE	MSE	Bias	ESE	MSE	Bias	ESE	MSE	EREa	Bias	ESE	MSE	Bias	ESE	MSE	EREa
100	0	0	0.003	0.284	0.081	0.003	0.284	0.080	0.004	0.280	0.078	−0.006	0.393	0.155	1.915	0.004	0.282	0.079	−0.006	0.393	0.155	1.915
		−0.2	−0.001	0.292	0.085	−0.002	0.289	0.084	0.003	0.287	0.082	−0.012	0.428	0.183	2.193	0.003	0.288	0.083	−0.013	0.428	0.183	2.193
		0.5	−0.020	0.342	0.118	−0.009	0.289	0.084	−0.018	0.324	0.105	−0.007	0.379	0.143	1.720	−0.018	0.329	0.109	−0.008	0.379	0.144	1.724
	0.3	0	0.003	0.318	0.101	0.002	0.313	0.098	0.004	0.313	0.098	−0.008	0.411	0.169	1.724	0.004	0.315	0.099	−0.007	0.411	0.169	1.313
		−0.2	−0.136	0.336	0.132	−0.010	0.332	0.110	−0.098	0.323	0.114	−0.023	0.467	0.219	1.979	−0.119	0.328	0.121	−0.024	0.467	0.219	1.979
		0.5	0.336	0.399	0.273	−0.003	0.323	0.104	0.231	0.352	0.177	0.002	0.385	0.149	1.421	0.300	0.367	0.225	0.011	0.393	0.155	1.480
	1	0	0.003	0.543	0.294	−0.001	0.521	0.271	0.004	0.536	0.288	−0.010	0.577	0.333	1.227	0.004	0.539	0.290	−0.010	0.577	0.333	1.227
		−0.2	−0.452	0.624	0.594	−0.029	0.587	0.345	−0.333	0.555	0.419	−0.048	0.687	0.475	1.370	−0.402	0.582	0.500	−0.050	0.686	0.473	1.366
		0.5	1.167	0.769	1.954	0.011	0.558	0.312	0.811	0.549	0.960	0.022	0.560	0.314	1.007	1.043	0.629	1.484	0.054	0.599	0.362	1.152
200	0	0	−0.004	0.203	0.041	−0.003	0.203	0.041	−0.002	0.202	0.041	−0.010	0.284	0.081	1.957	−0.003	0.202	0.041	−0.010	0.285	0.081	1.971
		−0.2	−0.004	0.213	0.045	−0.004	0.209	0.044	−0.001	0.210	0.044	−0.009	0.304	0.092	2.116	−0.001	0.211	0.044	−0.009	0.304	0.092	2.116
		0.5	0.001	0.258	0.067	0.004	0.202	0.041	−0.003	0.237	0.056	0.002	0.269	0.072	1.773	−0.001	0.243	0.059	0.001	0.269	0.072	1.773
	0.3	0	−0.007	0.227	0.052	−0.007	0.224	0.050	−0.006	0.225	0.051	−0.014	0.299	0.090	1.782	−0.006	0.226	0.051	−0.014	0.299	0.090	1.782
		−0.2	−0.140	0.246	0.080	−0.008	0.237	0.056	−0.099	0.235	0.065	−0.013	0.329	0.108	1.927	−0.121	0.239	0.072	−0.013	0.329	0.108	1.927
		0.5	0.378	0.305	0.236	0.006	0.220	0.048	0.255	0.255	0.130	0.007	0.271	0.073	1.517	0.326	0.267	0.178	0.010	0.270	0.073	1.506
	1	0	−0.014	0.389	0.152	−0.015	0.374	0.140	−0.015	0.386	0.149	−0.023	0.421	0.178	1.267	−0.014	0.388	0.150	−0.023	0.421	0.178	1.267
		−0.2	−0.457	0.462	0.422	−0.016	0.420	0.177	−0.328	0.405	0.272	−0.023	0.486	0.236	1.339	−0.401	0.428	0.344	−0.023	0.485	0.236	1.333
		0.5	1.257	0.602	1.943	0.012	0.369	0.136	0.856	0.389	0.884	0.018	0.379	0.144	1.055	1.089	0.449	1.386	0.031	0.377	0.143	1.044

Bias, ${\hat{\beta }}_1-{\beta }_1$, ${\beta }_1=1$; ESE, empirical sample error; MSE, mean-squared error; ERE, estimated relative efficiency.

^aEstimated relative efficiency was calculated for unbiased estimators with the variance of the Bůžková parameter estimate in the denominator.