Table 1:

Simulation results summarizing the estimates of the “slope” coefficient obtained by AME, LS, LAD, and ZQR, for both the AEPD and non-AEPD error distributions. This summary includes the average estimate minus the true value (Bias), relative efficiency (Eff), estimated coverage probability (Cov) associated with 95% confidence intervals, and averaged confidence interval length (AL). Here t₃ denotes Student’s t-distribution with 3 degrees of freedom; ${\chi }_3^2$ denotes a Chi-square distribution with 3 degrees of freedom; SN(4) denotes a skewed normal distribution with a slant parameter of 4; ST(3,0.5) for skewed t-distribution with 3 degrees of freedom and a skewing parameter of 0.5.

	N(0,1)				t3
	Bias	Eff	Cov	AL	Bias	Eff	Cov	AL
LS	0.0051	0.9741	0.960	0.2796	−0.0064	1.2331	0.954	0.4677
LAD	0.0037	1.2626	0.958	0.3598	−0.0036	1.0238	0.953	0.4042
ZQR	0.0037	1.2064	0.976	0.3765	−0.0028	1.0023	0.955	0.4174
AME	0.0053	1.0000	0.974	0.3104	−0.0023	1.0000	0.961	0.4238
	${\chi }_3^2$				Log-normal
LS	0.0053	2.3995	0.943	0.6811	−0.0017	1.4453	0.929	0.1665
LAD	−0.0016	2.5165	0.959	0.7644	−0.0028	1.4602	0.965	0.1814
ZQR	−0.0043	1.1525	0.977	0.4027	−0.0049	1.1287	0.963	0.1429
AME	−0.0030	1.0000	0.969	0.3426	−0.0032	1.0000	0.965	0.1276
	SN (4)				ST (3,0.5)
LS	−0.0014	1.0958	0.952	0.1768	−0.0224	2.0737	0.947	0.7030
LAD	−0.0020	1.4075	0.966	0.2276	−0.0081	1.4816	0.971	0.5871
ZQR	0.0004	1.2190	0.958	0.1988	−0.0066	1.0047	0.977	0.4375
AME	−0.0012	1.0000	0.942	0.1659	−0.0075	1.0000	0.979	0.4375
	Laplace				AEPD(0, 1.5, σ, 0.25)
LS	−0.0016	1.2904	0.942	0.2781	0.0037	1.3014	0.957	0.2780
LAD	−0.0028	0.9875	0.964	0.2347	0.0030	1.5021	0.979	0.3390
ZQR	−0.0042	0.9971	0.968	0.2434	0.0012	1.1321	0.973	0.2733
AME	−0.0044	1.0000	0.972	0.2562	0.0001	1.0000	0.965	0.2510