Table 3. Coverage rates (CR) at the nominal level of $5\mathrm{\%}$ and bias for different structure functions with $m_i={\mathrm{e}}^{0.1z_i}$ (true values of the parameters are in parentheses).

	$m_i=1$		$m_i=\rho z_i$		$m_i={\mathrm{e}}^{\rho z_i}$		$m_i=z_i^{\rho }$
Parameter	CR	bias	CR	bias	CR	bias	CR	bias
SN-HNLM
${\beta }_1(37)$	86.40	−0.12	87.94	0.11	94.64	−0.02	92.20	−0.06
${\beta }_2(43)$	90.08	−0.86	87.57	0.83	94.11	0.15	94.78	−0.06
${\beta }_3(0.6)$	94.04	−1.6${\mathrm{e}}^{-3}$	82.16	4.7${\mathrm{e}}^{-3}$	94.26	5.2${\mathrm{e}}^{-4}$	94.82	9.6${\mathrm{e}}^{-4}$
${\sigma }^2(0.5)$	5.02	0.61	81.97	−0.12	92.76	1.4${\mathrm{e}}^{-3}$	90.50	0.10
$\lambda (-3)$	92.04	−0.01	74.32	−1.16	95.85	−0.25	96.22	−0.30
$\rho (0.1)$	–	–	13.63	0.72	94.24	−4.9${\mathrm{e}}^{-4}$	18.47	0.26
StN-HNLM
${\beta }_1(37)$	93.04	−0.09	98.38	−0.04	92.13	−0.01	90.51	−0.04
${\beta }_2(43)$	95.11	−0.08	55.46	0.21	92.90	0.16	93.54	0.15
${\beta }_3(0.6)$	94.75	1.4${\mathrm{e}}^{-4}$	0.00	1.2${\mathrm{e}}^{-3}$	93.26	5.7${\mathrm{e}}^{-4}$	93.24	1.1${\mathrm{e}}^{-3}$
${\sigma }^2(0.5)$	77.59	0.50	62.94	−0.01	92.58	0.04	93.06	0.06
$\lambda (-3)$	93.56	0.04	27.73	−0.42	93.46	−0.49	93.71	−0.46
$\rho (0.1)$	–	–	85.65	0.35	94.38	−2.0${\mathrm{e}}^{-4}$	45.51	0.31
$\nu (3)$	96.85	−4.2${\mathrm{e}}^{-4}$	31.06	0.43	96.56	0.65	96.06	0.57
SSL-HNLM
${\beta }_1(37)$	79.16	−0.30	82.36	−0.10	96.14	−0.08	93.41	−0.08
${\beta }_2(43)$	82.23	1.07	71.59	1.91	95.34	0.19	98.12	0.29
${\beta }_3(0.6)$	56.83	3.9${\mathrm{e}}^{-3}$	75.67	6.8${\mathrm{e}}^{-3}$	95.05	1.7${\mathrm{e}}^{-3}$	96.89	1.6${\mathrm{e}}^{-3}$
${\sigma }^2(0.5)$	4.67	−0.05	0.00	41.68	95.54	0.04	94.91	0.04
$\lambda (-3)$	3.42	1.47	57.73	0.55	97.09	−0.25	96.89	−0.29
$\rho (0.1)$	–	–	0.00	−0.10	95.15	0.31	24.28	0.31
$\nu (3)$	0.00	−1.90	3.38	−0.96	92.62	3.89	90.21	4.63