Table 9 MSE of memory-type and proposed calibrated ratio estimators based on EWMA statistic at different values of correlation coefficient ρ, smoothing parameters \(\:\lambda\:=0.10,\:0.15,\:0.25,\) and sample sizes \(\:n\).

From: Innovative memory-type calibration estimators for better survey accuracy in stratified sampling

ρ	n	λ = 0.1		λ = 0.15		λ = 0.25
ρ	n	\(\:{{\stackrel{-}{y}}^{M}}_{pt}\)	\(\:{\widehat{y}}_{mp}\)	\(\:{{\stackrel{-}{y}}^{M}}_{pt}\)	\(\:{\widehat{y}}_{mp}\)	\(\:{{\stackrel{-}{y}}^{M}}_{pt}\)	\(\:{\widehat{y}}_{mp}\)
− 0.05	10	0.005633	0.000004	0.008491	0.000006	0.015184	0.000001
	20	0.002828	0.000002	0.004185	0.000003	0.007482	0.000005
	30	0.001941	0.000001	0.002812	0.000002	0.005094	0.000004
	50	0.001107	0.000000	0.001737	0.000001	0.003042	0.000002
	200	0.000280	0.000000	0.000429	0.000000	0.000758	0.000000
	500	0.000109	0.000000	0.000176	0.000000	0.000298	0.000000
− 0.25	10	0.005838	0.000004	0.009275	0.000006	0.016431	0.000001
	20	0.002982	0.000002	0.004553	0.000003	0.008280	0.000005
	30	0.002039	0.000002	0.003060	0.000001	0.005386	0.000003
	50	0.001224	0.000000	0.001868	0.000001	0.003284	0.000002
	200	0.000304	0.000000	0.000460	0.000000	0.000807	0.000000
	500	0.000124	0.000000	0.000188	0.000000	0.000325	0.000000
− 0.50	10	0.006472	0.000004	0.010138	0.000005	0.017557	0.000009
	20	0.003272	0.000002	0.004992	0.000003	0.008793	0.000005
	30	0.002140	0.000001	0.003386	0.000002	0.005954	0.000003
	50	0.001314	0.000000	0.002045	0.000001	0.003556	0.000002
	200	0.000335	0.000000	0.000505	0.000000	0.000871	0.000000
	500	0.000129	0.000000	0.000195	0.000000	0.000352	0.000000
− 0.75	10	0.007238	0.000003	0.011025	0.000005	0.019197	0.000009
	20	0.003477	0.000002	0.005311	0.000002	0.009607	0.000004
	30	0.002415	0.000001	0.003726	0.000002	0.006499	0.000003
	50	0.001380	0.000000	0.002202	0.000001	0.003757	0.000002
	200	0.000349	0.000000	0.000558	0.000000	0.000932	0.000000
	500	0.000137	0.000000	0.000223	0.000000	0.000381	0.000000
− 0.95	10	0.007437	0.000003	0.011555	0.000005	0.020780	0.000008
	20	0.003791	0.000002	0.005739	0.000002	0.009980	0.000004
	30	0.002431	0.000001	0.003820	0.000002	0.006730	0.000002
	50	0.001537	0.000000	0.002288	0.000001	0.004202	0.000002
	200	0.000381	0.000000	0.000568	0.000000	0.000999	0.000000
	500	0.000150	0.000000	0.000233	0.000000	0.000399	0.000000

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Table 9 MSE of memory-type and proposed calibrated ratio estimators based on EWMA statistic at different values of correlation coefficient ρ, smoothing parameters \(\:\lambda\:=0.10,\:0.15,\:0.25,\) and sample sizes \(\:n\).

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