Scientific Reports

Table 2 MSE of memory type estimators for chosen values of \(\rho _{xy}\), n, r, and \(\kappa\).

From: Optimal class of memory type imputation methods for time-based surveys using EWMA statistics

Strategies	\(\rho _{xy}\)	n	r	\(\kappa =0.1\)				\(\kappa =0.5\)				\(\kappa =0.9\)
Strategy 1	\(\rho _{xy}\)	n	r	\(t_{r_1}^m\)	\(t_i^m,~i=1,4\)	\(t_{s_1}^m\)	\(t_{s_4}^m\)	\(t_{r_1}^m\)	\(t_i^m,~i=1,4\)	\(t_{s_1}^m\)	\(t_{s_4}^m\)	\(t_{r_1}^m\)	\(t_i^m,~i=1,4\)	\(t_{s_1}^m\)	\(t_{s_4}^m\)
	0.1	15	12	17139.050	1.301	1.267	1.284	108547.300	8.242	7.413	8.397	266434.300	20.231	16.480	16.806
		15	14	982.720	1.114	1.093	1.062	6223.895	7.057	6.489	6.516	15276.830	17.321	14.630	14.830
		150	120	0.234	0.124	0.124	0.124	1.482	0.787	0.783	0.783	3.638	1.933	1.909	1.908
		150	140	0.213	0.104	0.104	0.104	1.346	0.660	0.657	0.657	3.304	1.620	1.603	1.602
		300	240	0.097	0.054	0.054	0.054	0.615	0.341	0.341	0.341	1.516	0.838	0.834	0.834
		300	280	0.087	0.044	0.044	0.044	0.549	0.277	0.277	0.277	1.347	0.683	0.677	0.677
	0.5	15	12	1778.345	1.035	1.014	1.015	11262.850	6.557	6.032	6.039	27645.170	16.093	13.661	13.048
		15	14	155.791	0.852	0.840	0.825	986.679	5.393	5.063	5.365	2421.848	13.237	11.623	11.195
		150	120	0.145	0.099	0.099	0.099	0.919	0.629	0.627	0.626	2.256	1.544	1.529	1.524
		150	140	0.125	0.08	0.080	0.080	0.792	0.505	0.504	0.503	1.943	1.241	1.231	1.227
		300	240	0.061	0.043	0.043	0.043	0.388	0.275	0.275	0.275	0.953	0.676	0.673	0.672
		300	280	0.051	0.034	0.034	0.034	0.325	0.213	0.213	0.213	0.798	0.523	0.522	0.521
	0.9	15	12	218789.200	0.471	0.466	1.182	1385665.000	2.986	2.859	7.337	3401178.000	7.329	6.721	17.549
		15	14	75.371	0.276	0.275	0.304	477.351	1.751	1.708	1.789	1171.679	4.298	4.081	4.134
		150	120	0.052	0.046	0.046	0.046	0.328	0.292	0.291	0.291	0.806	0.716	0.713	0.711
		150	140	0.032	0.026	0.026	0.026	0.202	0.166	0.166	0.166	0.497	0.408	0.407	0.406
		300	240	0.024	0.021	0.021	0.021	0.150	0.136	0.136	0.136	0.368	0.333	0.333	0.332
		300	280	0.014	0.012	0.012	0.012	0.087	0.073	0.073	0.073	0.213	0.179	0.179	0.179

Strategy 2				\(t_{r_2}^m\)	\(t_i^m,~i=2,5\)	\(t_{s_2}^m\)	\(t_{s_5}^m\)	\(t_{r_2}^m\)	\(t_i^m,~i=2,5\)	\(t_{s_2}^m\)	\(t_{s_5}^m\)	\(t_{r_2}^m\)	\(t_i^m,~i=2,5\)	\(t_{s_2}^m\)	\(t_{s_5}^m\)
	0.1	15	12	21488.700	1.274	1.240	1.315	136095.100	8.069	7.265	7.429	334051.600	19.806	16.167	16.342
		15	14	1053.896	1.108	1.086	1.145	6674.675	7.014	6.451	6.618	16383.290	17.217	14.550	8.539
		150	120	0.266	0.124	0.124	0.124	1.684	0.785	0.781	0.781	4.134	1.928	1.904	1.902
		150	140	0.222	0.104	0.104	0.104	1.403	0.660	0.657	0.657	3.444	1.619	1.602	1.601
		300	240	0.112	0.054	0.054	0.054	0.712	0.341	0.340	0.341	1.748	0.837	0.832	0.832
		300	280	0.091	0.044	0.044	0.044	0.576	0.277	0.277	0.277	1.414	0.680	0.677	0.677
	0.5	15	12	2229.356	0.953	0.934	0.961	14119.250	6.035	5.573	5.017	34656.350	14.812	12.668	12.022
		15	14	167.004	0.829	0.817	0.824	1057.694	5.249	4.932	4.114	2596.157	12.883	11.335	10.945
		150	120	0.152	0.093	0.093	0.093	0.964	0.588	0.586	0.585	2.366	1.444	1.431	1.425
		150	140	0.127	0.078	0.078	0.078	0.804	0.494	0.492	0.492	1.973	1.212	1.203	1.199
		300	240	0.065	0.040	0.040	0.040	0.409	0.255	0.255	0.255	1.003	0.627	0.624	0.623
		300	280	0.052	0.033	0.033	0.033	0.331	0.207	0.207	0.207	0.812	0.509	0.508	0.507
	0.9	15	12	274319.100	0.243	0.241	1.119	1737354	1.541	1.497	7.129	4264415.000	3.781	3.575	17.148
		15	14	80.752	0.211	0.210	0.233	511.428	1.339	1.312	1.405	1255.323	3.288	3.148	2.917
		150	120	0.031	0.024	0.024	0.024	0.198	0.150	0.150	0.150	0.485	0.368	0.367	0.366
		150	140	0.026	0.020	0.020	0.020	0.165	0.126	0.126	0.126	0.405	0.309	0.309	0.308
		300	240	0.013	0.010	0.010	0.010	0.084	0.065	0.065	0.065	0.207	0.160	0.160	0.159
		300	280	0.011	0.008	0.008	0.008	0.068	0.053	0.053	0.053	0.167	0.130	0.130	0.130

Strategy 3				\(t_{r_3}^m\)	\(t_i^m,~i=3,6\)	\(t_{s_3}^m\)	\(t_{s_6}^m\)	\(t_{r_3}^m\)	\(t_i^m,~i=3,6\)	\(t_{s_3}^m\)	\(t_{s_6}^m\)	\(t_{r_3}^m\)	\(t_i^m,~i=3,6\)	\(t_{s_3}^m\)	\(t_{s_6}^m\)
	0.1	15	12	4351.064	1.382	1.344	1.358	27556.740	8.751	7.842	7.928	67639.260	21.481	17.374	17.331
		15	14	72.382	1.200	1.176	1.176	458.422	7.600	6.960	6.946	1125.217	18.654	15.631	15.671
		150	120	0.157	0.125	0.125	0.125	0.997	0.792	0.788	0.788	2.447	1.945	1.920	1.920
		150	140	0.114	0.105	0.105	0.105	0.723	0.666	0.663	0.663	1.776	1.634	1.617	1.617
		300	240	0.072	0.054	0.054	0.054	0.447	0.343	0.342	0.342	1.081	0.841	0.836	0.836
		300	280	0.048	0.044	0.044	0.044	0.306	0.279	0.278	0.278	0.752	0.684	0.681	0.681
	0.5	15	12	452.371	1.278	1.247	1.260	2865.018	8.091	7.342	7.209	7032.317	19.860	16.413	16.256
		15	14	12.379	1.143	1.123	1.123	78.398	7.239	6.687	6.673	192.432	17.769	15.102	15.054
		150	120	0.128	0.115	0.115	0.115	0.812	0.727	0.724	0.723	1.994	1.784	1.764	1.763
		150	140	0.103	0.100	0.100	0.100	0.655	0.631	0.629	0.629	1.608	1.549	1.534	1.534
		300	240	0.056	0.049	0.049	0.049	0.352	0.311	0.311	0.311	0.863	0.764	0.761	0.761
		300	280	0.043	0.042	0.042	0.042	0.275	0.263	0.263	0.263	0.675	0.647	0.644	0.644
	0.9	15	12	55531.280	1.142	1.118	1.298	351698.100	7.235	6.629	7.758	863258.900	17.758	14.937	17.635
		15	14	6.553	1.108	1.089	1.089	41.504	7.015	6.491	6.493	101.874	17.219	14.689	14.679
		150	120	0.101	0.100	0.100	0.100	0.642	0.631	0.629	0.629	1.576	1.550	1.535	1.534
		150	140	0.096	0.096	0.096	0.096	0.609	0.606	0.604	0.604	1.495	1.488	1.474	1.474
		300	240	0.042	0.042	0.042	0.042	0.268	0.263	0.263	0.262	0.658	0.645	0.643	0.643
		300	280	0.041	0.040	0.040	0.040	0.252	0.251	0.251	0.250	0.619	0.615	0.613	0.613

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