Table 4.

Simulation results of estimating equations (a)–(e) for case 2 where linearity condition (2) is violated when n = 250, d_γ = 5 and d_β = 10^†

Estimator	Parameter	γ1 (%)	γ2 (%)	γ3 (%)	γ4 (%)	γ5 (%)	β1(%)	β2(%)	β5(%)
(a)	bias	187.83	64.28	32.53	0.69	0.34	−18.25	−3.89	23.04
	std	73.24	53.39	17.42	35.13	38.64	12.46	11.53	14.24
	mse	40645.36	6983.39	1361.69	1234.67	1493.53	488.42	148.09	733.60
(b)	bias	−0.83	0.53	0.05	0.21	26.34	−20.78	−3.60	25.01
	std	38.21	22.40	7.73	12.35	19.77	13.44	11.54	14.63
	mse	1460.43	502.20	59.76	152.60	1084.49	612.39	146.11	839.40
Oracle	bias	−0.03	0.50	0.15	0.41	26.56	−20.83	−3.58	25.04
	std	42.51	23.54	8.39	13.14	20.75	13.46	11.56	14.64
	mse	1806.81	554.54	70.48	172.89	1135.78	615.05	146.46	841.32
(c)	bias	0.48	0.17	−0.09	−0.20	−0.80	−0.90	−0.60	−0.14
	std	23.57	13.10	4.83	7.34	9.25	2.15	5.28	4.42
	mse	555.96	171.68	23.34	53.92	86.17	5.44	28.25	19.59
Oracle	bias	0.57	0.22	−0.13	−0.21	−0.75	−0.92	−0.63	−0.04
	std	23.49	13.07	4.85	7.29	9.17	2.19	5.29	4.55
	mse	551.97	170.79	23.53	53.21	84.69	5.66	28.40	20.75
(d)	bias	0.25	0.49	−0.06	−0.08	−0.16	−0.71	−0.27	0.27
	std	21.68	12.44	4.45	6.97	8.13	1.39	4.36	2.92
	mse	470.15	155.02	19.81	48.61	66.06	2.43	19.08	8.61
Oracle	bias	−0.38	0.33	0.11	0.28	16.23	−15.95	−3.47	14.28
	std	25.71	15.44	5.41	8.69	11.96	9.41	14.33	10.15
	mse	661.40	238.64	29.26	75.62	406.37	342.74	217.35	306.85
(e)	bias	0.31	0.44	−0.06	−0.10	−0.22	−0.67	−0.22	−0.34
	std	21.79	12.43	4.43	6.98	8.11	1.41	4.42	3.09
	mse	475.10	154.77	19.61	48.68	65.89	2.43	19.55	9.66
Oracle	bias	0.03	0.19	−0.05	−0.10	−0.11	−0.72	−0.15	−0.24
	std	19.24	11.12	3.87	6.28	7.37	1.47	4.34	3.39
	mse	370.22	123.67	14.99	39.46	54.35	2.69	18.87	11.58

^†The oracle estimates of (b)–(e) assume that the link function g and its first derivative g′ are known.