Abstract
In a two-sample model, we introduce the normal theory statistical procedures, non-parametric procedures based on ranks and the semi-parametric procedures possessing the robustness of Huber (1964). After the computational algorithm of the permutation tests for their test procedures is given, the powers of the three test procedures are compared due to a simulation. The computational algorithm for the semi-parametric estimators is also given. The mean squared errors for the three-type estimators are compared through a simulation. It can be seen that, (i) when the underlying distribution is in a neighbourhood of the normal distribution, the semi-parametric procedures is superior to the parametric procedures and the non-parametric procedures, and (ii) when the underlying distribution is not in a neighbourhood of the normal distribution, the non-parametric procedures are superior. By using the bootstrap estimate of the variances for the tree-type estimators based on real data, we may give the best choice among the three statistical procedures. However we point out that the bootstrap choice is sometimes mistaken. Furthermore, by using a simulation of 1000 replicates, we can see that the bootstrap estimate of the relative effiency among the estimators is fairly different from the value of the real relative efficiency.
