Table 3.

Simulation results of estimating equations (a)–(e) for case 1 where linearity condition (2) is satisfied when n = 250, d_γ = 5 and d_β = 10^†

Estimator	Parameter	γ1 (%)	γ2 (%)	γ3 (%)	γ4 (%)	γ5 (%)	β1(%)	β2(%)	β5(%)
(a)	bias	189.56	63.33	31.82	0.72	0.39	−5.66	−0.59	−1.23
	std	56.03	40.14	13.50	26.16	29.27	5.91	12.23	11.33
	mse	39073.67	5622.59	1194.71	684.93	857.03	66.97	149.94	129.78
(b)	bias	−0.45	0.29	0.15	0.00	4.17	−5.67	−0.62	−1.10
	std	27.34	16.19	5.67	9.17	11.64	5.81	12.04	11.02
	mse	747.82	262.35	32.12	84.06	152.93	65.84	145.44	122.57
Oracle	bias	−0.43	0.39	0.17	−0.03	4.20	−5.67	−0.62	−1.10
	std	27.44	16.46	5.71	9.23	11.82	5.82	12.04	11.03
	mse	753.23	271.04	32.67	85.12	157.34	66.00	145.28	122.84
(c)	bias	0.00	0.23	−0.05	−0.33	−0.74	−0.76	−0.55	−0.40
	std	23.67	13.46	4.78	7.45	9.18	2.10	5.29	4.86
	mse	560.16	181.34	22.88	55.67	84.88	4.98	28.31	23.80
Oracle	bias	−0.13	0.22	−0.06	−0.30	−0.80	−0.76	−0.57	−0.45
	std	23.47	13.38	4.76	7.50	9.23	2.10	5.28	4.87
	mse	550.80	179.12	22.63	56.29	85.85	5.00	28.24	23.94
(d)	bias	0.10	0.36	−0.08	−0.13	−0.35	−0.64	−0.31	−0.08
	std	22.34	12.59	4.52	7.08	8.23	1.45	4.15	3.90
	mse	499.22	158.59	20.44	50.20	67.78	2.52	17.35	15.21
Oracle	bias	0.13	0.31	0.01	0.20	7.38	−9.17	−1.79	−2.52
	std	24.53	14.68	5.16	8.14	10.77	7.73	15.29	14.04
	mse	601.92	215.64	26.61	66.31	170.42	143.85	236.98	203.48
(e)	bias	0.18	0.34	−0.09	−0.13	−0.35	−0.65	−0.34	−0.09
	std	22.35	12.63	4.50	7.06	8.18	1.47	4.24	3.93
	mse	499.37	159.56	20.29	49.87	67.06	2.60	18.10	15.42
Oracle	bias	0.23	0.30	−0.09	−0.10	−0.22	−0.69	−0.13	−0.10
	std	19.45	11.12	3.91	6.28	7.34	1.53	4.25	3.72
	mse	378.44	123.85	15.31	39.40	53.89	2.83	18.06	13.84

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