Table 5.

Empirical power of profile least square ratio test T_n and the Wald test W_n at level 0.05 for hypothesis (4.5). Data were generated from models (4.1) with β = (0.2, c − 1.2, 1)^T and c ∈ {0, 0.1, 0.2, 0.25, 0.5, 0.7, 1} and α₁(u) and α₂(u) given by (4.2) and (4.4), respectively. The methods used are “Asm” for the asymptotic version, and “Boot” for the bootstrap version.

		Tn			Wald
c		B	P	N	B	P	N
0	Aym	0.060	0.070	0.080	0.050	0.050	0.080
	Boot	0.050	0.060	0.060	0.060	0.060	0.060
0.10	Aym	0.150	0.140	0.150	0.130	0.130	0.150
	Boot	0.130	0.100	0.080	0.130	0.120	0.080
0.20	Aym	0.190	0.220	0.120	0.150	0.150	0.120
	Boot	0.170	0.160	0.080	0.190	0.180	0.080
0.25	Aym	0.350	0.340	0.240	0.320	0.310	0.240
	Boot	0.290	0.280	0.180	0.310	0.300	0.180
0.50	Aym	0.740	0.710	0.530	0.670	0.660	0.530
	Boot	0.700	0.630	0.500	0.720	0.630	0.500
0.70	Aym	0.940	0.940	0.870	0.930	0.920	0.870
	Boot	0.920	0.890	0.800	0.930	0.890	0.800
1.00	Aym	1.000	1.000	1.000	0.990	0.990	1.000
	Boot	0.990	0.990	0.960	0.990	0.990	0.960