Restrictive adaptive tests for the treatment of the two-sample scale problem

Abstract The two-sample scale problem is studied using special restrictive adaptive methods. A two-stage procedure is proposed. The first stage is based on order statistics and the second stage is based on rank statistics. We use transformations of order statistics which are dependent on measures of tailweight and skewness of distributions. These measures are estimated by quantiles. Adaptive tests are derived on the basis of the asymptotic relative efficiences of the rank tests. It is shown by simulation experiments that these methods are also suitable for moderate sample sizes.