An affine invariant rank-based method for comparing dependent groups

A basic property of various rank-based hypothesis testing methods is that they are invariant under a linear transformation of the data. For multivariate data, a generalization of this property is sometimes sought (called affine invariance), but typically techniques for assigning ranks do not achieve this goal, or it is assumed that sampling is from a symmetric distribution. A rank-based method is suggested for comparing dependent groups that is based on halfspace depth, is affine invariant in terms of difference scores, and allows sampling from asymmetric distributions.