Table 1. Summary statistics for the simulation studies under H(x) = G(x) = x.

n		ϕ = 1				ϕ = 0				ϕ = −1
		Bias	SE	SEE	CP	Bias	SE	SEE	CP	Bias	SE	SEE	CP
200	α1	−0.009	0.183	0.183	0.95	−0.000	0.176	0.170	0.93	0.000	0.204	0.203	0.94
	α2	−0.003	0.160	0.154	0.94	−0.006	0.148	0.143	0.95	0.007	0.175	0.171	0.95
	A(τ/4)	0.003	0.100	0.099	0.94	0.005	0.111	0.108	0.94	0.006	0.071	0.070	0.95
	A(τ/2)	0.001	0.129	0.130	0.95	0.007	0.148	0.143	0.94	0.009	0.094	0.093	0.95
	A(3τ/4)	−0.009	0.206	0.209	0.95	0.012	0.231	0.224	0.94	0.018	0.146	0.145	0.95
	β1	0.005	0.244	0.245	0.96	0.025	0.189	0.194	0.95	0.016	0.240	0.254	0.96
	β2	0.018	0.192	0.198	0.96	0.029	0.160	0.161	0.95	0.024	0.195	0.202	0.96
	Λ(τ/4)	0.002	0.067	0.067	0.96	−0.007	0.050	0.051	0.96	0.002	0.062	0.065	0.96
	Λ(τ/2)	0.004	0.104	0.106	0.96	−0.005	0.081	0.083	0.97	0.003	0.098	0.098	0.96
	Λ(3τ/4)	0.036	0.264	0.257	0.96	0.007	0.171	0.180	0.96	0.009	0.224	0.224	0.96
	ϕ	0.034	0.359	0.377	0.96	0.003	0.211	0.213	0.95	−0.013	0.405	0.462	0.95
	${\sigma }_b^2$	−0.017	0.136	0.144	0.98	−0.021	0.119	0.123	0.97	−0.021	0.172	0.169	0.97
400	α1	−0.000	0.133	0.130	0.94	−0.000	0.122	0.120	0.94	0.005	0.139	0.144	0.96
	α2	0.004	0.112	0.109	0.95	0.002	0.100	0.101	0.96	0.004	0.122	0.121	0.94
	A(τ/4)	−0.000	0.070	0.070	0.95	0.000	0.079	0.076	0.94	0.000	0.047	0.049	0.96
	A(τ/2)	−0.002	0.092	0.092	0.95	0.001	0.106	0.100	0.94	0.001	0.062	0.065	0.96
	A(3τ/4)	−0.013	0.154	0.147	0.95	0.006	0.165	0.158	0.94	0.004	0.096	0.102	0.96
	β1	0.009	0.168	0.171	0.96	0.015	0.136	0.134	0.95	0.008	0.178	0.178	0.95
	β2	0.011	0.138	0.138	0.95	0.012	0.111	0.111	0.96	0.008	0.145	0.141	0.95
	Λ(τ/4)	−0.001	0.046	0.047	0.95	−0.004	0.037	0.036	0.95	0.001	0.045	0.046	0.95
	Λ(τ/2)	−0.002	0.174	0.074	0.95	−0.005	0.060	0.058	0.95	0.000	0.070	0.069	0.95
	Λ(3τ/4)	−0.002	0.170	0.171	0.95	0.001	0.126	0.125	0.96	0.005	0.171	0.157	0.94
	ϕ	0.007	0.239	0.249	0.97	0.001	0.139	0.141	0.95	0.014	0.293	0.305	0.94
	${\sigma }_b^2$	−0.002	0.101	0.103	0.96	−0.005	0.088	0.087	0.96	−0.006	0.118	0.121	0.97

Note: Bias and SE are the bias and standard error of the parameter estimator, SEE is the mean of the standard error estimator, and CP is the coverage probability of the 95% confidence interval. The confidence intervals for A(·) and Λ(·) are constructed on the basis of the log transformation, while the confidence intervals for ${\sigma }_b^2$ are based on the Satterthwaite approximation: $\left(\nu {\widehat{\sigma }}_b^2/{\chi }_{\nu ,0.975}^2,\nu {\widehat{\sigma }}_b^2/{\chi }_{\nu ,0.025}^2\right)$, where $\nu =2{\left\{{\widehat{\sigma }}_b^2/\widehat{\text{se}}\left({\widehat{\sigma }}_b^2\right)\right\}}^2$, and ${\chi }_{\nu ,\alpha }^2$ is the α-quantile of the χ²-distribution with ν degrees of freedom.