Project Euclid

A robustified version of the two sample sign test is defined which is insensitive to certain deviations from the assumption of the independence of the observations. These deviations are described in terms of mixing conditions. The asymptotic value of the power function of this robustified sign test is computed on contiguous alternatives possessing the same dependence structure. This entails the calculation of its asymptotic relative efficiencies with respect to some tests which are optimal on these alternatives in the independent case. It becomes apparent that in general the relative performance of two tests heavily depends on the structure of dependence of the observations, i.e. it may either increase or decrease.