De beleidstechnische aspecten van standaardisatie als wiskundig vraagstuk

Abstract

The approach introduced by Chernoff and Savage to prove asymptotic normality under fixed alternatives of rank statistics for the two-sample problem has first been applied, in a suitably modified form, by Bhuchongkul to probe asymptotic normality of rank statistics for testing the hypothesis of independence. In the present tract this method is generalized so that weaker conditions on the limiting score function suffice for the asymptotic normality under fixed continuous bivariate distribution functions,belonging to the alternative. The condition frequently encountered in the literature that the limiting score function, which is a function on the unit interval is abandoned. Apart from this secondary generalization, the main results lie in an essential enlargement of the orders of magnitude of the limiting score function near the boundary of the unit square, and in the fact that unit square, parallel to the axes. Discontinuity of the limiting score function entails, however, a local differentiability condition on the underlying bivariate distribution function. The presentation of the material is selfcontained.