Locally most powerful rank tests

Abstract

It is the purpose of this present paper to introduce a new concept of locally most powerful rank tests. In the sequel we obtain finite sample results undervery mild regularity conditions. The approach is more v general than the related treatment of Hájek and Šidák (1967). In contrast to those authors, we need no assumptions concerning the derivatives of the underlying denstities. For instance, in the case of a regression problem in location, the density of the location family must be only square integrable. Thus the results also apply to discontinuous densities. We treat hypotheses H. of the following kind against parametric alternatives; H₀, H₁(secttest of symmetry) and H(test of independence).