. 2021 Apr 24;49(5):1323–1347. doi: 10.1080/02664763.2021.1913103

Table 3.

Empirical mean, median, SE, SD, LCL and UCL for the indicated values of n, λ (negative) and SNAR model parameters with simulated data.

		n = 250				n = 500				n = 1000
		SNAR(1)	SNAR(2)	SNAR(3)	SNAR(4)	SNAR(1)	SNAR(2)	SNAR(3)	SNAR(4)	SNAR(1)	SNAR(2)	SNAR(3)	SNAR(4)
$ϕ_{1}$	True value	0.7	1.2	1.2	1.2	0.7	1.2	1.2	1.2	0.7	1.2	1.2	1.2
	Mean	0.699615	1.198326	1.213548	1.200235	0.698168	1.199453	1.213583	1.194775	0.69886	1.199512	1.213028	1.196481
	Median	0.700765	1.1989	1.2127	1.2024	0.6988	1.19995	1.2155	1.19435	0.699925	1.20025	1.2146	1.1969
	SE (mean)	0.002322	0.002083	0.002679	0.002843	0.001554	0.001488	0.001859	0.002051	0.001096	0.001054	0.001311	0.001428
	SD	0.03671	0.032928	0.04236	0.04496	0.034755	0.033281	0.041571	0.045863	0.034671	0.033315	0.041462	0.045151
	LCL (mean)	0.695042	1.194224	1.208271	1.194634	0.695114	1.196529	1.20993	1.190745	0.696709	1.197445	1.210455	1.19368
	UCL (mean)	0.704188	1.202428	1.218824	1.205835	0.701222	1.202377	1.217235	1.198805	0.701012	1.201579	1.215601	1.199283
$ϕ_{2}$	True value	–	$-$ 0.7	$-$ 0.7	$-$ 0.7	–	$-$ 0.7	$-$ 0.7	$-$ 0.7	–	$-$ 0.7	$-$ 0.7	$-$ 0.7
	Mean	–	$-$ 0.69775	$-$ 0.70746	$-$ 0.7051	–	$-$ 0.69979	$-$ 0.70653	$-$ 0.69861	–	$-$ 0.69895	$-$ 0.7058	$-$ 0.69989
	Median	–	$-$ 0.69962	$-$ 0.71058	$-$ 0.70333	–	$-$ 0.70102	$-$ 0.70822	$-$ 0.69693	–	$-$ 0.7009	$-$ 0.70752	$-$ 0.69955
	SE (mean)	–	0.002081	0.003723	0.004271	–	0.001492	0.002612	0.003114	–	0.001035	0.001872	0.00215
	SD	–	0.032898	0.058872	0.067529	–	0.033372	0.058415	0.069637	–	0.032721	0.059192	0.067987
	LCL (mean)	–	$-$ 0.70184	$-$ 0.71479	$-$ 0.71351	–	−0.70272	−0.71166	−0.70473	–	−0.70098	−0.70948	−0.70411
	UCL (mean)	–	$-$ 0.69365	$-$ 0.70013	$-$ 0.69668	–	$-$ 0.69685	$-$ 0.7014	$-$ 0.69249	–	$-$ 0.69692	$-$ 0.70213	$-$ 0.69568
$ϕ_{3}$	True value	–	–	0.3	0.3	–	–	0.3	0.3	–	–	0.3	0.3
	Mean	–	–	0.315807	0.303356	–	–	0.314438	0.297795	–	–	0.313783	0.299921
	Median	–	–	0.314665	0.310225	–	–	0.313535	0.298625	–	–	0.313285	0.301375
	SE (Mean)	–	–	0.002738	0.004257	–	–	0.001815	0.00305	–	–	0.001343	0.00212
	SD	–	–	0.043287	0.067311	–	–	0.04059	0.068199	–	–	0.042484	0.067036
	LCL (mean)	–	–	0.310415	0.294972	–	–	0.310872	0.291802	–	–	0.311147	0.295761
	UCL (mean)	–	–	0.321199	0.311741	–	–	0.318005	0.303787	–	–	0.31642	0.30408
$ϕ_{4}$	True value	–	–	–	0.1	–	–	–	0.1	–	–	–	0.1
	Mean	–	–	–	0.092073	–	–	–	0.094778	–	–	–	0.092742
	Median	–	–	–	0.087778	–	–	–	0.09487	–	–	–	0.091923
	SE (mean)	–	–	–	0.00276	–	–	–	0.001907	–	–	–	0.001365
	SD	–	–	–	0.043637	–	–	–	0.042643	–	–	–	0.043178
	LCL (mean)	–	–	–	0.086638	–	–	–	0.091032	–	–	–	0.090063
	UCL (mean)	–	–	–	0.097509	–	–	–	0.098525	–	–	–	0.095422
σ	True value	1	1	1	1	1	1	1	1	1	1	1	1
	Mean	0.996724	0.957133	0.995972	0.993711	0.998946	0.95831	0.993768	0.994974	0.997188	0.961357	0.99203	0.992205
	Median	0.983695	0.957005	0.91776	0.99086	0.984435	0.95706	0.921825	0.98631	0.98663	0.962865	0.92203	0.986255
	SE (mean)	0.00691	0.003752	0.003562	0.004166	0.005794	0.002725	0.002538	0.003573	0.003678	0.002016	0.001811	0.002348
	SD	0.109252	0.059324	0.056327	0.065878	0.129558	0.060922	0.056746	0.0799	0.116302	0.063755	0.057266	0.074242
	LCL (mean)	0.983115	0.949743	0.988955	0.985505	0.987562	0.952957	0.988692	0.987953	0.989971	0.957401	0.988476	0.987598
	UCL (mean)	1.010333	0.964523	1.022988	1.001917	1.010329	0.963663	0.998844	1.001994	1.004405	0.965314	0.995584	0.996812
λ	True value	−0.1	−0.2	−0.15	−0.05	−0.1	−0.2	−0.15	−0.05	−0.1	−0.2	−0.15	−0.05
	Mean	−0.10255	−0.19768	−0.14649	−0.05109	−0.10439	−0.19926	−0.14716	−0.05493	−0.1004	−0.19903	−0.14841	−0.05039
	Median	−0.08814	−0.19579	−0.15483	−0.03529	−0.09185	−0.1993	−0.15698	−0.0336	−0.09214	−0.20017	−0.15622	−0.03282
	SE (mean)	0.008548	0.006831	0.003232	0.005423	0.006292	0.004599	0.002337	0.00455	0.004016	0.003163	0.001678	0.002827
	SD	0.135153	0.10801	0.051104	0.085748	0.1407	0.102829	0.052261	0.101746	0.126994	0.100037	0.053062	0.089388
	LCL (mean)	−0.11939	−0.21114	−0.15286	−0.06177	−0.11675	−0.20829	−0.15175	−0.06387	−0.10828	−0.20524	−0.1517	−0.05593
	UCL (mean)	−0.08572	−0.18423	−0.14013	−0.04041	−0.09202	−0.19022	−0.14256	−0.04599	−0.09252	−0.19282	−0.14512	−0.04484