Table 1.

Simulation Results: Performance of test for regression parameter under the null

row	N	pi(θ0)	E(n)	Ê (D̂1)	ESD	wi(θ̂) treated as estimated		wi(θ̂) treated as fixed
						ASE	ESL	ASE	ESL
1	100	0.25	62.5	−0.008	0.224	0.201	2.1%	0.112	28.4%
2		0.50	75	0.001	0.119	0.118	3.1%	0.051	38.3%
3		0.75	87.5	−0.003	0.064	0.065	3.4%	0.024	50.2%
4	500	0.25	312.5	−0.003	0.085	0.087	3.6%	0.029	55.3%
5		0.50	375	−0.001	0.047	0.046	4.0%	0.011	66.0%
6		0.75	437.5	0.000	0.026	0.026	4.8%	0.005	77.4%
7	1000	0.25	625	0.000	0.058	0.059	4.3%	0.015	63.5%
8		0.50	750	−0.001	0.032	0.033	4.4%	0.006	72.6%
9		0.75	875	−0.000	0.018	0.019	3.8%	0.002	80.0%

p_i(θ₀) = P (I_i = 1|Z_i1 = 1, Zi₃ ∈ (0, 4])

ESD = empirical standard deviation

ASE = average asymptotic standard error

ESL = empirical significance level.