Table 5 MSEs of product estimators for ${\lambda }_{2}$=0.03.

From: Combination of memory type ratio and product estimators under extended EWMA statistic with application to wheat production

$\lambda_{1}$		$0.1$		$0.15$		$0.25$		$0.5$		$0.75$		$1$
Ρ	n	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}$	$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}$
− 0.05	10	0.0038	0.0028	0.0082	0.0069	0.0148	0.0137	0.0339	0.0332	0.0624	0.0621	0.1030	0.1030
	20	0.0019	0.0014	0.0041	0.0035	0.0072	0.0066	0.0169	0.0166	0.0305	0.0304	0.0511	0.0511
	30	0.0012	0.0009	0.0027	0.0023	0.0047	0.0044	0.0111	0.0109	0.0204	0.0203	0.0338	0.0338
	50	0.0007	0.0005	0.0016	0.0013	0.0028	0.0026	0.0068	0.0066	0.0123	0.0122	0.0204	0.0204
	200	0.0002	0.0001	0.0004	0.0003	0.0007	0.0006	0.0017	0.0016	0.0030	0.0030	0.0051	0.0051
	500	0.0000	0.0000	0.0001	0.0001	0.0003	0.0002	0.0006	0.0006	0.0012	0.0012	0.0020	0.0020
− 0.25	10	0.0049	0.0036	0.0078	0.0066	0.0131	0.0121	0.0309	0.0303	0.0572	0.0570	0.0946	0.0946
	20	0.0024	0.0018	0.0037	0.0031	0.0068	0.0062	0.0156	0.0153	0.0282	0.0281	0.0463	0.0463
	30	0.0016	0.0012	0.0024	0.0021	0.0044	0.0041	0.0104	0.0101	0.0186	0.0186	0.0314	0.0314
	50	0.0009	0.0007	0.0015	0.0012	0.0027	0.0025	0.0062	0.0061	0.0112	0.0112	0.0187	0.0187
	200	0.0002	0.0001	0.0004	0.0003	0.0006	0.0006	0.0015	0.0015	0.0028	0.0027	0.0047	0.0047
	500	0.0000	0.0000	0.0001	0.0001	0.0002	0.0002	0.0006	0.0006	0.0011	0.0011	0.0018	0.0018
− 0.50	10	0.0043	0.0032	0.0067	0.0057	0.0120	0.0111	0.0283	0.0277	0.0502	0.0500	0.0842	0.0842
	20	0.0026	0.0017	0.0034	0.0028	0.0059	0.0054	0.0138	0.0135	0.0251	0.0250	0.0421	0.0421
	30	0.0014	0.0011	0.0022	0.0018	0.0040	0.0037	0.0093	0.0091	0.0167	0.0167	0.0278	0.0278
	50	0.0009	0.0006	0.0013	0.0011	0.0023	0.0021	0.0056	0.0054	0.0101	0.0100	0.0167	0.0167
	200	0.0002	0.0001	0.0003	0.0002	0.0006	0.0005	0.0013	0.0013	0.0025	0.0025	0.0041	0.0041
	500	0.0000	0.0000	0.0001	0.0001	0.0002	0.0002	0.0005	0.0005	0.0010	0.0009	0.0016	0.0016
− 0.75	10	0.0038	0.0028	0.0060	0.0051	0.0107	0.0098	0.0245	0.0240	0.0445	0.0443	0.0739	0.0739
	20	0.0019	0.0014	0.0029	0.0025	0.0052	0.0048	0.0124	0.0121	0.0224	0.0223	0.0370	0.0370
	30	0.0012	0.0009	0.0020	0.0017	0.0035	0.0032	0.0081	0.0079	0.0148	0.0147	0.0248	0.0248
	50	0.0007	0.0005	0.0011	0.0009	0.0020	0.0019	0.0049	0.0048	0.0088	0.0088	0.0147	0.0147
	200	0.0002	0.0001	0.0003	0.0002	0.0005	0.0004	0.0012	0.0012	0.0022	0.0022	0.0036	0.0036
	500	0.0000	0.0000	0.0001	0.0001	0.0002	0.0001	0.0004	0.0004	0.0008	0.0008	0.0014	0.0014
− 0.95	10	0.0035	0.0026	0.0053	0.0045	0.0093	0.0086	0.0219	0.0214	0.0397	0.0395	0.0658	0.0658
	20	0.0017	0.0013	0.0026	0.0022	0.0047	0.0043	0.0110	0.0108	0.0196	0.0195	0.0329	0.0329
	30	0.0011	0.0008	0.0018	0.0015	0.0031	0.0029	0.0074	0.0072	0.0132	0.0132	0.0218	0.0218
	50	0.0007	0.0005	0.0010	0.0009	0.0018	0.0017	0.0044	0.0043	0.0078	0.0078	0.0132	0.0132
	200	0.0002	0.0001	0.0002	0.0002	0.0004	0.0004	0.0011	0.0010	0.0019	0.0019	0.0033	0.0033
	500	0.0000	0.0000	0.0001	0.0000	0.0001	0.0001	0.0004	0.0004	0.0007	0.0007	0.0013	0.0013

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Table 5 MSEs of product estimators for \({\lambda }_{2}\)=0.03.

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\(\lambda_{1}\)		\(0.1\)		\(0.15\)		\(0.25\)		\(0.5\)		\(0.75\)		\(1\)
Ρ	n	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{rmi}\)	\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}{t}_{ermi}\)
− 0.05	10	0.0038	0.0028	0.0082	0.0069	0.0148	0.0137	0.0339	0.0332	0.0624	0.0621	0.1030	0.1030
	20	0.0019	0.0014	0.0041	0.0035	0.0072	0.0066	0.0169	0.0166	0.0305	0.0304	0.0511	0.0511
	30	0.0012	0.0009	0.0027	0.0023	0.0047	0.0044	0.0111	0.0109	0.0204	0.0203	0.0338	0.0338
	50	0.0007	0.0005	0.0016	0.0013	0.0028	0.0026	0.0068	0.0066	0.0123	0.0122	0.0204	0.0204
	200	0.0002	0.0001	0.0004	0.0003	0.0007	0.0006	0.0017	0.0016	0.0030	0.0030	0.0051	0.0051
	500	0.0000	0.0000	0.0001	0.0001	0.0003	0.0002	0.0006	0.0006	0.0012	0.0012	0.0020	0.0020
− 0.25	10	0.0049	0.0036	0.0078	0.0066	0.0131	0.0121	0.0309	0.0303	0.0572	0.0570	0.0946	0.0946
	20	0.0024	0.0018	0.0037	0.0031	0.0068	0.0062	0.0156	0.0153	0.0282	0.0281	0.0463	0.0463
	30	0.0016	0.0012	0.0024	0.0021	0.0044	0.0041	0.0104	0.0101	0.0186	0.0186	0.0314	0.0314
	50	0.0009	0.0007	0.0015	0.0012	0.0027	0.0025	0.0062	0.0061	0.0112	0.0112	0.0187	0.0187
	200	0.0002	0.0001	0.0004	0.0003	0.0006	0.0006	0.0015	0.0015	0.0028	0.0027	0.0047	0.0047
	500	0.0000	0.0000	0.0001	0.0001	0.0002	0.0002	0.0006	0.0006	0.0011	0.0011	0.0018	0.0018
− 0.50	10	0.0043	0.0032	0.0067	0.0057	0.0120	0.0111	0.0283	0.0277	0.0502	0.0500	0.0842	0.0842
	20	0.0026	0.0017	0.0034	0.0028	0.0059	0.0054	0.0138	0.0135	0.0251	0.0250	0.0421	0.0421
	30	0.0014	0.0011	0.0022	0.0018	0.0040	0.0037	0.0093	0.0091	0.0167	0.0167	0.0278	0.0278
	50	0.0009	0.0006	0.0013	0.0011	0.0023	0.0021	0.0056	0.0054	0.0101	0.0100	0.0167	0.0167
	200	0.0002	0.0001	0.0003	0.0002	0.0006	0.0005	0.0013	0.0013	0.0025	0.0025	0.0041	0.0041
	500	0.0000	0.0000	0.0001	0.0001	0.0002	0.0002	0.0005	0.0005	0.0010	0.0009	0.0016	0.0016
− 0.75	10	0.0038	0.0028	0.0060	0.0051	0.0107	0.0098	0.0245	0.0240	0.0445	0.0443	0.0739	0.0739
	20	0.0019	0.0014	0.0029	0.0025	0.0052	0.0048	0.0124	0.0121	0.0224	0.0223	0.0370	0.0370
	30	0.0012	0.0009	0.0020	0.0017	0.0035	0.0032	0.0081	0.0079	0.0148	0.0147	0.0248	0.0248
	50	0.0007	0.0005	0.0011	0.0009	0.0020	0.0019	0.0049	0.0048	0.0088	0.0088	0.0147	0.0147
	200	0.0002	0.0001	0.0003	0.0002	0.0005	0.0004	0.0012	0.0012	0.0022	0.0022	0.0036	0.0036
	500	0.0000	0.0000	0.0001	0.0001	0.0002	0.0001	0.0004	0.0004	0.0008	0.0008	0.0014	0.0014
− 0.95	10	0.0035	0.0026	0.0053	0.0045	0.0093	0.0086	0.0219	0.0214	0.0397	0.0395	0.0658	0.0658
	20	0.0017	0.0013	0.0026	0.0022	0.0047	0.0043	0.0110	0.0108	0.0196	0.0195	0.0329	0.0329
	30	0.0011	0.0008	0.0018	0.0015	0.0031	0.0029	0.0074	0.0072	0.0132	0.0132	0.0218	0.0218
	50	0.0007	0.0005	0.0010	0.0009	0.0018	0.0017	0.0044	0.0043	0.0078	0.0078	0.0132	0.0132
	200	0.0002	0.0001	0.0002	0.0002	0.0004	0.0004	0.0011	0.0010	0.0019	0.0019	0.0033	0.0033
	500	0.0000	0.0000	0.0001	0.0000	0.0001	0.0001	0.0004	0.0004	0.0007	0.0007	0.0013	0.0013