ABSTRACT

Table I presents the simulation results. In the simulation study, the type I errors are slightly larger than the theoretical values of 0.05 and 0.0 I. Departures from the theoretical values are severe for the small sample sizes. For example, type I errors are 0.06 and 0.02 instead of 0.05 and 0.0 I, respectively when n = 20. This can be also observed from Fig. I. Figure l indicates that

N 0.0624 0.0330 0.0532 0.0257 0.0519 0.0216 0.0527 0.0168 L 0.1771 0.1163 0.2111 0.1401 0.2732 0.1789 0.4107 0.2734 c 0.9162 0.8921 0.9810 0.9705 0.9988 0.9981 1.0000 1.0000 f 3 0.4462 0.3675 0.5765 0.4905 0.7460 0.6620 0.9331 0.8871 I 5 0.2642 0.1944 0.3356 0.2489 0.4540 0.3480 0.6662 0.5459

N: normal distribution; L: logistic distribution; C: Cauchy distribution; tk: t distribution with k degrees of freedom

for small sample sizes the asymptotic distribution is slightly skewed to the right. As a result of this, the type I error becomes larger.