Table 2.

(Linear regression model) Empirical relative efficiency of OWQAE with estimated optimal weight compared to five methods: OLS, LAD, QAU, QAO, CQR. 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].

(a): Model 1 in (56)
εt	n = 100					n = 300
Distribution	OLS	LAD	QAU	QAO	CQR	OLS	LAD	QAU	QAO	CQR
Student-t1	NA	0.86	2.55	0.74	1.11	NA	1.04	3.16	0.89	1.37
Student-t2	NA	0.95	1.14	0.81	0.89	NA	1.06	1.30	0.99	1.02
N(0,1)	0.86	1.33	0.90	0.90	0.91	0.89	1.43	0.95	0.95	0.97
Mixture 1	5.10	0.89	3.70	0.77	1.45	7.79	1.27	6.12	0.95	2.00
Mixture 2	2.22	10.85	2.31	1.18	2.03	2.65	19.88	2.84	1.09	2.30
Laplace	1.24	0.85	1.06	0.85	0.89	1.48	0.87	1.23	0.87	1.01
Gamma(1)	5.69	5.46	4.81	0.67	2.51	7.09	6.98	6.12	0.76	2.91
Gamma(2)	2.08	2.60	1.96	0.88	1.48	2.23	2.85	2.14	0.94	1.61
Gamma(3)	1.49	2.02	1.48	0.92	1.25	1.64	2.21	1.61	0.99	1.35
Beta(1,1)	1.49	4.20	1.73	0.91	1.77	1.58	4.58	1.88	0.95	1.90
Beta(1,2)	1.71	3.65	1.93	1.09	1.71	2.02	4.47	2.34	1.97	1.99
Beta(1,3)	2.39	4.30	2.59	1.36	2.01	2.78	5.12	3.06	3.03	2.25

(b): Model 2 in (57), n = 300
εt	β1					β2
Distribution	OLS	LAD	QAU	QAO	CQR	OLS	LAD	QAU	QAO	CQR
Student-t1	NA	1.00	1.85	0.89	1.28	NA	0.85	2.74	0.80	1.07
Student-t2	NA	1.10	1.19	1.04	0.99	NA	1.04	1.23	1.13	1.00
N(0,1)	0.91	1.45	0.94	0.94	0.98	0.90	1.36	0.94	0.94	0.95
Mixture 1	6.85	1.14	4.84	0.92	1.78	6.82	1.16	5.20	0.88	1.77
Mixture 2	2.70	19.79	2.86	1.11	2.35	2.80	19.51	2.99	1.18	2.43
Laplace	1.36	0.89	1.17	0.89	0.99	1.37	0.91	1.21	0.91	1.00
Gamma(1)	6.70	6.23	5.38	0.79	2.83	6.24	6.22	5.35	0.75	2.80
Gamma(2)	2.39	2.94	2.22	0.95	1.70	2.42	2.80	2.23	0.93	1.68
Gamma(3)	1.53	1.95	1.50	0.97	1.27	1.68	2.07	1.59	0.91	1.36
Beta(1,1)	1.50	4.30	1.79	0.93	1.80	1.50	4.15	1.77	0.94	1.81
Beta(1,2)	1.92	4.24	2.21	0.86	1.95	2.23	4.89	2.52	0.85	2.21
Beta(1,3)	2.78	4.71	3.04	0.82	2.29	2.77	4.60	3.01	0.80	2.28