Table 2.

Bias estimates of the three standard error estimators (SE₁, SE₂, SE₃) when the covariance structure of a 2-component Gaussian mixture is assumed to be conditionally independent based on 1000 replications under each mixture distribution with m = 5, γ₁ = γ₂ = 0, β₁ = 1, V₁ = I_m, ${\sigma }_1^2=0.25$, β₂ = 3, V₂ = V (ρ) and ${\sigma }_2^2=1$ where V (ρ) is the exchangeable correlation matrix. Approximate standard error is based on the estimated standard deviation of the simulation distribution. Values equal to zero represent values less than 0.001.

Bias Estimates
ρ	n	${\widehat{\mathit{SE}}}_1({\widehat{\gamma }}_1)$	${\widehat{\mathit{SE}}}_2({\widehat{\gamma }}_1)$	${\widehat{\mathit{SE}}}_3({\widehat{\gamma }}_1)$	${\widehat{\mathit{SE}}}_1({\widehat{\beta }}_1)$	${\widehat{\mathit{SE}}}_2({\widehat{\beta }}_1)$	${\widehat{\mathit{SE}}}_3({\widehat{\beta }}_1)$	${\widehat{\mathit{SE}}}_1({\widehat{\sigma }}_1^2)$	${\widehat{\mathit{SE}}}_2({\widehat{\sigma }}_1^2)$	${\widehat{\mathit{SE}}}_3({\widehat{\sigma }}_1^2)$
0.00	100	0.007	0.007	0.007	0.000	0.001	−0.000	−0.001	0.001	−0.001
	500	0.002	0.002	0.002	−0.000	0.000	−0.000	0.000	0.000	0.000
	1000	0.001	0.001	0.001	0.000	0.000	0.000	0.000	0.000	0.000
0.50	100	0.004	0.004	0.004	−0.006	−0.008	−0.002	−0.007	−0.009	−0.004
	500	0.002	0.002	0.002	−0.003	−0.004	−0.001	−0.002	−0.004	−0.001
	1000	−0.001	−0.001	−0.001	−0.002	−0.002	−0.000	−0.001	−0.002	−0.000
0.99	100	−0.003	−0.003	−0.002	−0.026	−0.035	−0.010	−0.013	−0.016	−0.008
	500	−0.005	−0.005	−0.004	−0.011	−0.015	−0.003	−0.005	−0.007	−0.002
	1000	−0.003	−0.003	−0.002	−0.007	−0.010	−0.001	−0.003	−0.005	−0.002
ρ	n				${\widehat{\mathit{SE}}}_1({\widehat{\beta }}_2)$	${\widehat{\mathit{SE}}}_2({\widehat{\beta }}_2)$	${\widehat{\mathit{SE}}}_3({\widehat{\beta }}_2)$	${\widehat{\mathit{SE}}}_1({\widehat{\sigma }}_2^2)$	${\widehat{\mathit{SE}}}_2({\widehat{\sigma }}_2^2)$	${\widehat{\mathit{SE}}}_3({\widehat{\sigma }}_2^2)$
0.00	100				0.001	0.003	0.001	−0.008	−0.004	−0.010
	500				0.001	0.001	0.001	0.001	0.001	0.000
	1000				0.000	0.000	0.000	0.001	0.001	0.001
0.50	100				−0.046	−0.070	−0.005	−0.019	−0.028	−0.004
	500				−0.021	−0.032	−0.002	−0.010	−0.016	−0.001
	1000				−0.014	−0.021	−0.000	−0.009	−0.013	−0.002
0.99	100				−0.092	−0.122	−0.017	−0.085	−0.111	−0.022
	500				−0.040	−0.054	−0.006	−0.035	−0.049	−0.003
	1000				−0.027	−0.037	−0.002	−0.026	−0.036	−0.004