. Author manuscript; available in PMC: 2010 Sep 22.

Published in final edited form as: Scand Stat Theory Appl. 2009 Sep 22;37(1):126–146. doi: 10.1111/j.1467-9469.2009.00661.x

Table 3.

Parameter estimates under exceptional laws: summary statistics of g-estimation using Zeroing Instead of Plugging In (ZIPI) and the usual g-estimates from 1000 datasets of sample sizes 250, 500 and 1000 using 80%, 90%, and 95% CIs for ZIPI. Second interval parameter estimates are omitted for all but 80% CI exclusions since the exclusions affect only first-interval parameters when using ZIPI (see section 3.2).

CI exclusion		ZIPI					Usual g-estimation
CI exclusion	ψ^†	Mean(ψ̂)	SE	\|t\|^a	rMSE	Cov.^b	Mean(ψ̂)	SE	\|t\|^a	rMSE	Cov.^b
n = 250
80%	ψ₁₀ = 1.6	1.631	0.167	0.174	0.229	94.3	1.659	0.179	0.322	0.243	95.7
	ψ₁₁ = 0.0	−0.001	0.042	0.031	0.057	94.3	−0.001	0.042	0.029	0.057	94.6
	ψ₂₀ = −3.0	−2.991	0.299	0.016	0.413	92.8	−2.991	0.299	0.016	0.413	93.3
	ψ₂₁ = 2.0	1.977	0.325	0.095	0.461	92.3	1.977	0.325	0.095	0.461	92.4
	ψ₂₂ = 1.0	0.992	0.444	0.020	0.606	94.2	0.992	0.444	0.020	0.606	94.3
	ψ₂₃ = 0.0	0.014	0.505	0.015	0.696	93.1	0.014	0.505	0.015	0.696	93.4
90%	ψ₁₀ = 1.6	1.622	0.165	0.126	0.227	94.3
	ψ₁₁ = 0.0	−0.001	0.042	0.031	0.057	94.1
95%	ψ₁₀ = 1.6	1.617	0.164	0.098	0.225	94.4
	ψ₁₁ = 0.0	−0.001	0.042	0.030	0.057	94.2
n = 500
80%	ψ₁₀ = 1.6	1.615	0.118	0.108	0.164	92.6	1.636	0.126	0.281	0.172	94.2
	ψ₁₁ = 0.0	0.000	0.030	0.003	0.041	94.8	0.000	0.030	0.002	0.041	94.7
	ψ₂₀ = −3.0	−2.998	0.212	0.006	0.288	93.5	−2.998	0.212	0.006	0.288	94.1
	ψ₂₁ = 2.0	1.993	0.233	0.047	0.317	93.7	1.993	0.233	0.047	0.317	93.9
	ψ₂₂ = 1.0	0.996	0.314	0.013	0.432	93.9	0.996	0.314	0.013	0.432	94.3
	ψ₂₃ = 0.0	−0.002	0.360	0.018	0.495	93.3	−0.002	0.360	0.018	0.495	93.7
90%	ψ₁₀ = 1.6	1.609	0.117	0.062	0.161	93.2
	ψ₁₁ = 0.0	0.000	0.030	0.003	0.041	94.9
95%	ψ₁₀ = 1.6	1.605	0.116	0.032	0.160	93.3
	ψ₁₁ = 0.0	0.000	0.030	0.002	0.041	94.9
n = 1000
80%	ψ₁₀ = 1.6	1.616	0.083	0.180	0.114	94.9	1.632	0.090	0.348	0.121	95.3
	ψ₁₁ = 0.0	−0.001	0.021	0.041	0.028	94.8	−0.001	0.021	0.042	0.028	95.1
	ψ₂₀ = −3.0	−2.995	0.150	0.025	0.207	93.4	−2.995	0.150	0.025	0.207	93.7
	ψ₂₁ = 2.0	1.997	0.165	0.030	0.225	93.8	1.997	0.165	0.030	0.225	94.0
	ψ₂₂ = 1.0	0.992	0.222	0.036	0.305	94.2	0.992	0.222	0.036	0.305	94.5
	ψ₂₃ = 0.0	0.003	0.255	0.003	0.348	94.8	0.003	0.255	0.003	0.348	95.0
90%	ψ₁₀ = 1.6	1.611	0.083	0.127	0.113	95.1
	ψ₁₁ = 0.0	−0.001	0.021	0.042	0.028	94.8
95%	ψ₁₀ = 1.6	1.608	0.082	0.089	0.112	95.1
	ψ₁₁ = 0.0	−0.001	0.021	0.042	0.028	94.7

|t| = |Bias(ψ̂)/SE(ψ̂)|

Coverage of 95% Wald confidence intervals