Bias

SSE

ASE

CP

 

(nD, nD) = (100, 100)

 a0

2.4%

0.163

0.151

94.8%

a1

2.2%

0.085

0.083

95.4%

R(0.2)

0.4%

0.039

0.039

94.6%

R(0.4)

0.3%

0.032

0.031

93.4%

R(0.7)

0.1%

0.025

0.023

90.8%

 

(nD, nD) = (100, 50)

a0

0.9%

0.159

0.157

95.0%

a1

2.9%

0.088

0.088

94.6%

R(0.2)

-0.3%

0.041

0.042

94.6%

R(0.4)

-0.1%

0.033

0.033

94.6%

R(0.7)

-0.1%

0.025

0.024

93.8%

 

(nD, nD) = (50, 100)

 a0

1.1%

0.205

0.208

96.4%

a1 

0.9%

0.101

0.113

97.2%

R(0.2)

-0.2%

0.053

0.053

93.8%

R(0.4)  

-0.2%

0.041

0.043

94.4%

R(0.7)  

-0.3%

0.030

0.033

94.6%

Table 5: Result of 1000 simulations to evaluate the application of inference based on asymptotic theory to finite sample studies. (α0, α1) = (1.2, 0.45). Relative bias = bias / true value x 100%; SSE: sampling standard error; ASE: mean estimated standard error using asymptotic theory; CP: coverage of 95% Wald-confidence intervals using estimated asymptotic error.