Table 3.

(Nonlinear regression model) Empirical relative efficiency of OWQAE with estimated weights compared to four methods: OLS, LAD, QAU, QAO. Mixture 1: 0.5N(0,1)+0.5N(0,0.5⁶); Mixture 2: 0.5N(−2,1)+0.5N(2,1). For Student-t₁, t₂, due to infinite variance, the OLS is not stable and varies significantly in simulations. [Numbers ≥ 1 indicate better performance of OWQAE].

	Model 3 in (58)				Model 4 in (59)
εt	β = 0.6				β1 = 0.3				β2 = 0.5
Distribution	OLS	LAD	QAU	QAO	OLS	LAD	QAU	QAO	OLS	LAD	QAU	QAO
Student-t1	NA	0.48	1.61	0.55	NA	0.75	2.06	0.74	NA	0.73	2.38	0.75
Student-t2	NA	1.00	1.37	1.55	NA	1.02	1.23	0.91	NA	0.99	1.21	1.06
N(0,1)	0.79	1.81	0.96	0.95	0.97	1.45	0.99	0.99	0.92	1.38	0.97	0.97
Mixture 1	3.75	1.01	3.16	0.86	6.45	1.12	4.62	0.89	6.99	1.09	5.08	0.91
Mixture 2	1.81	9.54	1.90	1.02	2.56	16.83	2.72	1.15	2.75	18.08	2.85	1.15
Laplace	1.36	1.19	1.15	1.19	1.52	0.93	1.28	0.93	1.42	0.89	1.21	0.89
Gamma(1)	4.21	6.58	3.94	0.75	6.74	6.42	5.78	0.77	6.67	6.44	5.56	0.73
Gamma(2)	1.71	2.78	1.69	0.97	2.23	2.59	2.07	0.97	2.39	2.90	2.21	0.92
Gamma(3)	1.31	1.89	1.28	1.14	1.59	2.04	1.53	0.96	1.64	2.05	1.58	0.92
Beta(1,1)	1.15	4.61	1.98	0.94	1.67	4.48	1.95	0.93	1.57	4.02	1.82	0.94
Beta(1,2)	1.08	3.72	1.97	2.50	1.98	3.98	2.24	0.89	2.06	4.21	2.30	0.85
Beta(1,3)	1.58	4.38	2.93	5.27	2.84	4.85	3.02	0.81	2.96	4.94	3.09	0.89