TABLE 3.

Unconditional inferences for binary outcomes:(w₁, w₂, w₃, w₄) = (0.242, 0.045, 0.526, 0.187)′ and π = 1/3. (τ₁₁, τ₁₂, τ₁₃, τ₁₄) = (0.717, 0.900, 0.602, 0.750) and (τ₂₁, τ₂₂, τ₂₃, τ₂₄) = (0.615, 0.750, 0.815, 0.880). Bias stands for the empirical bias. ESE stands for the empirical standard errors. CP1 and CP2 stand for the empirical coverage levels of upper and lower 97.5% confidence intervals, respectively. $\widehat{P}\left(\left|b_{\pi w}\right|>SE/3\right)$ is the empirical probability that the absolute bias is greater than one third of the standard error of the naive estimator

n	θ	Bias	ESE	CP1	CP2	$\widehat{P}\left(\left|b_{\pi w}\right|>SE/3\right)$
302	$\widehat{\theta }$	−0.013	0.289	0.974	0.978	0.108
	${\widehat{\theta }}_{\pi w}$	−0.013	0.286	0.972	0.975
	${\widehat{\theta }}_{\text{new}}$	−0.011	0.286	0.972	0.975
	${\widehat{\theta }}_S$	−0.012	0.286	0.976	0.979
723	$\widehat{\theta }$	−0.008	0.184	0.976	0.976	0.118
	${\widehat{\theta }}_{\pi w}$	−0.008	0.181	0.976	0.976
	${\widehat{\theta }}_{\text{new}}$	−0.008	0.181	0.976	0.976
	${\widehat{\theta }}_S$	−0.005	0.182	0.976	0.978
3894	$\widehat{\theta }$	−0.001	0.079	0.975	0.976	0.119
	${\widehat{\theta }}_{\pi w}$	−0.001	0.077	0.974	0.975
	${\widehat{\theta }}_{\text{new}}$	−0.001	0.077	0.974	0.975
	${\widehat{\theta }}_S$	0.004	0.078	0.973	0.980