Table 5.

(Nonparametric regression model) Empirical relative efficiency of the local least-absolute-deviation estimator (LAD), Kai, Li and Zou (2010)’s local CQR estimator, and the proposed OWQAE, relative to the benchmark local LS estimator. For CQR and OWQAE: τ_j = j/(k + 1), j = 1, …, k, k = 9, 19, 29.

(a): Model 7 in (64)
			CQR, k =			OWQAE, k =
Distribution of ε	LS	LAD	9	19	29	9	19	29
N(0,1)	1	0.73	0.99	1.00	0.99	0.96	0.95	0.95
Truncated N(0,1) on [−1, 1]	1	0.54	0.93	0.98	0.99	1.14	1.25	1.26
Truncated Cauchy on [−10, 10]	1	1.67	1.16	1.07	1.05	1.40	1.27	1.21
Truncated Cauchy on [−1, 1]	1	0.53	0.93	0.98	0.99	1.07	1.20	1.20
Student-t with 3 d.f.’s	1	1.44	1.39	1.21	1.16	1.42	1.28	1.19
Standard Laplace	1	1.26	1.11	1.06	1.05	1.16	1.10	1.06
Uniform on [−0.5, 0.5]	1	0.51	0.94	0.98	0.99	1.23	1.24	1.21
0.5N(−2,1)+0.5N(2,1)	1	0.31	0.92	0.97	0.99	1.57	1.60	1.62
0.95N(0,1)+0.05N(0,9)	1	0.88	1.13	1.08	1.06	1.05	0.98	0.95

(b): Model 8 in (65)
			CQR, k =			OWQAE, k =
Distribution of ε	LS	LAD	9	19	29	9	19	29
N(0,1)	1	0.66	0.96	0.98	0.98	0.94	0.95	0.95
Truncated N(0,1) on [−1, 1]	1	0.43	0.84	0.91	0.93	1.14	1.56	1.80
Truncated Cauchy on [−10, 10]	1	2.39	1.35	1.17	1.12	1.97	1.78	1.61
Truncated Cauchy on [−1, 1]	1	0.46	0.84	0.91	0.94	1.02	1.35	1.55
Student-t with 3 d.f.’s	1	1.73	1.75	1.52	1.41	1.72	1.51	1.44
Standard Laplace	1	1.48	1.18	1.11	1.09	1.31	1.24	1.16
Uniform on [−0.5, 0.5]	1	0.36	0.84	0.91	0.94	1.46	2.21	2.70
0.5N(−2,1)+0.5N(2,1)	1	0.20	0.88	0.95	0.97	2.12	2.18	2.17
0.95N(0,1)+0.05N(0,9)	1	0.86	1.18	1.15	1.12	1.10	1.02	0.95