Table 1.

Simulation Results for ÂB_opt; BT represent back-transformed confidence intervals while DT represents delta-theorem based confidence intervals

Simulation	1	2	3	4	5	6	7
n	1000	1000	1000	1000	1000	1000	1000
Reps	10000	10000	10000	10000	10000	10000	10000
α0	−1.25	−1.25	−1.25	−1.25	−1	0.25	−1.25
α1	2	2	2	0	−1	1	2
β0	−2.5	−2.5	−2.5	−2.5	1	−2	−2.5
β1	1.25	1.25	1.25	1.25	1	0.75	0
β2	1.1	1.1	1.1	1.1	1	1.2	1.1
β3	0	2	−1	−2	−1	1.5	0
P(T = 1)	0.318	0.318	0.318	0.223	0.303	0.551	0.318
P(Y = 1)	0.184	0.263	0.122	0.143	0.786	0.304	0.111
P{Y*(0) = 1}	0.111	0.111	0.111	0.111	0.697	0.164	0.111
P{Y*(1) = 1}	0.267	0.363	0.223	0.2545	0.881	0.169	0.111
P{Y*(gopt) = 1}	0.111	0.108	0.1	0.068	0.691	0.348	0.111
ABdom	0.396	0.577	0.094	0.223	0.113	0.446	0
ABopt	0.396	0.588	0.184	0.523	0.121	0.461	0
${\widehat{AB}}_{\mathit{opt}}(0)$	0.3953	0.5897	0.1982	0.5277	0.1251	0.4627	0.1073
$\widehat{SE}\{A{B}_{\mathit{opt}}(0)\}mc$	0.0799	0.0584	0.0605	0.0538	0.0168	0.0632	0.0773
$\widehat{SE}\{A{B}_{\mathit{opt}}(0)\}dt$	0.0786	0.0578	0.0593	0.0536	0.0169	0.0626	0.0944
BT Lower 95%	0.2195	0.4587	0.0720	0.4098	0.0914	0.3245	−0.1024
BT Upper 95%	0.5310	0.6885	0.3055	0.6218	0.1574	0.5723	0.2715
BT Coverage	0.9415	0.9428	0.9477	0.9492	0.9579	0.9455	0.9320
DT Lower 95%	0.2413	0.4764	0.0820	0.4226	0.0920	0.3400	−0.0776
DT Upper 95%	0.5493	0.7030	0.3144	0.6328	0.1581	0.5855	0.2922
DT Coverage	0.9384	0.9352	0.9420	0.9418	0.9568	0.9420	0.8897