Table 10 MSE of memory-type and proposed calibrated ratio estimators based on EWMA statistic at different values of correlation coefficient ρ, smoothing parameters \(\:\lambda\:=0.50,\:0.75,\:1.00,\) and sample sizes \(\:n\).

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

ρ	n	λ = 0.50		λ = 0.75		λ = 1.00
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	0.035752	0.000025	0.063054	0.000004	0.105316	0.000075
	20	0.017522	0.000012	0.031670	0.000022	0.053501	0.000038
	30	0.011821	0.000008	0.021123	0.000015	0.035537	0.000025
	50	0.007111	0.000005	0.012642	0.000009	0.021145	0.000015
	200	0.001757	0.000001	0.003162	0.000002	0.005311	0.000004
	500	0.000703	0.000000	0.001282	0.000001	0.002115	0.000002
− 0.25	10	0.038048	0.000023	0.068815	0.000042	0.115304	0.000071
	20	0.018849	0.000012	0.034376	0.000021	0.057268	0.000035
	30	0.012711	0.000008	0.023094	0.000014	0.037734	0.000023
	50	0.007593	0.000047	0.013591	0.000008	0.022993	0.000014
	200	0.001911	0.000001	0.003396	0.000002	0.005721	0.000004
	500	0.000768	0.000000	0.001368	0.000001	0.002287	0.000001
− 0.50	10	0.040971	0.000022	0.073906	0.000038	0.123899	0.000064
	20	0.020640	0.000011	0.037184	0.000019	0.061697	0.000032
	30	0.013831	0.000007	0.024630	0.000013	0.041739	0.000022
	50	0.008296	0.000004	0.014952	0.000008	0.024880	0.000013
	200	0.002089	0.000001	0.003725	0.000002	0.006138	0.000003
	500	0.000834	0.000000	0.001493	0.000001	0.002496	0.000001
− 0.75	10	0.044780	0.000011	0.081238	0.000036	0.133767	0.000058
	20	0.022196	0.000010	0.040066	0.000018	0.066787	0.000029
	30	0.011482	0.000006	0.026627	0.000012	0.044253	0.000019
	50	0.008846	0.000004	0.016090	0.000007	0.026514	0.000011
	200	0.002230	0.000001	0.004026	0.000002	0.006645	0.000003
	500	0.000897	0.000000	0.001616	0.000001	0.002676	0.000001
− 0.95	10	0.046862	0.000018	0.084832	0.000032	0.141350	0.000053
	20	0.023610	0.000009	0.042147	0.000016	0.071195	0.000027
	30	0.015585	0.000006	0.028655	0.000011	0.047536	0.000018
	50	0.009454	0.000004	0.017143	0.000007	0.028471	0.000011
	200	0.002333	0.000001	0.004229	0.000002	0.007157	0.000003
	500	0.000953	0.000000	0.001710	0.000001	0.002853	0.000001

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Table 10 MSE of memory-type and proposed calibrated ratio estimators based on EWMA statistic at different values of correlation coefficient ρ, smoothing parameters \(\:\lambda\:=0.50,\:0.75,\:1.00,\) and sample sizes \(\:n\).

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