Table II.

Simulation results for the comparison of jackknife method and BRR method for variance estimates under STSCS design, ρ =0 or 0.2.

θ	t	Bias1*	Bias2*	Bias(BRR1)	Bias(BRR2)	Bias(JK1)	Bias(JK2)	RMSE1	RMSE2
ρ = 0
0.9	1200	0.0002	0.0044	1.0103	1.1212	1.0103	1.0505	0.0097	0.0108
	800	−0.0003	0.0070	1.0336	1.2195	1.0336	1.0894	0.0119	0.0142
	400	0.0004	0.0172	1.1059	1.2813	1.0765	1.1711	0.0170	0.0254
0.8	1200	−0.0006	0.0032	1.0519	1.0949	1.0519	1.0730	0.0135	0.0141
	800	0.0004	0.0069	1.0058	1.1086	1.0058	1.0457	0.0172	0.0188
	400	−0.0008	0.0136	1.0398	1.1416	1.0199	1.0892	0.0251	0.0301
0.7	1200	0.0004	0.0037	1.0184	1.0606	1.0184	1.0424	0.0163	0.0169
	800	0.0001	0.0056	1.0049	1.0870	1.0049	1.0531	0.0203	0.0215
	400	0.0005	0.0122	1.0279	1.1677	0.9930	1.0968	0.0287	0.0333
0.6	1200	0.0023	0.0034	1.0479	1.0447	1.0060	1.0279	0.0169	0.0182
	800	0.0042	0.0044	1.1472	1.0848	1.0508	1.0670	0.0201	0.0229
	400	0.0134	0.0103	1.2370	1.1722	1.1575	1.1057	0.0287	0.0347
ρ = 0.2
0.9	1200	−0.0108	−0.0062	1.1715	1.2805	1.1102	1.2000	0.0160	0.0171
	800	−0.0126	−0.0152	1.1750	1.3086	1.0809	1.2057	0.0185	0.0231
	400	−0.0134	−0.0189	1.2751	1.3633	1.1005	1.2245	0.0231	0.0309
0.8	1200	−0.0115	−0.0066	1.1553	1.2623	1.0987	1.1882	0.0191	0.0197
	800	−0.0121	−0.0168	1.2111	1.2963	1.1122	1.2130	0.0217	0.0273
	400	−0.0137	−0.0176	1.2323	1.3115	1.1181	1.2230	0.0289	0.0352
0.7	1200	−0.0084	−0.0053	1.1219	1.2103	1.0698	1.1495	0.0191	0.0201
	800	−0.0091	−0.0113	1.1900	1.2516	1.0950	1.1911	0.0220	0.0252
	400	−0.0102	−0.0145	1.2610	1.4058	1.1397	1.2981	0.0291	0.0344
0.6	1200	−0.0027	0.0022	1.2108	1.2632	1.0723	1.1368	0.0168	0.0191
	800	0.0083	−0.0038	1.2741	1.2937	1.1015	1.1429	0.0214	0.0241
	400	0.0109	−0.0058	1.2857	1.3050	1.2231	1.1880	0.0274	0.0356

Note:

^*1 = unweighted estimator, 2 = weighted estimator.

$\text{Bias}1=\widehat{\theta }1-\theta$, $\text{Bias}2=\widehat{\theta }2-\theta$, Bias(BRR1) = SE(BRR1)/SE(EMP1), Bias(BRR2) = SE(BRR2)/SE(EMP2), Bias(JK1)=SE(JK1)/SE(EMP1), Bias(JK2)=SE(JK2)/SE(EMP2), SE = standard error, EMP = empirical variance estimates, RMSE = root of mean squared error.