A simpler, affine-invariant, multivariate, distribution-free sign test

A simpler multivariate sign test is proposed that uses the transformation-retransformation approach of Chakraborty, Chaudhuri, and Oja together with a directional transformation due to Tyler. This produces a multivariate sign test that is practical to apply to data of any dimension, makes minimal assumptions about the underlying distribution, and has a small-sample distribution-free property over a broad class of population models. It is shown to perform very well in comparison to Hotelling's T-2 and other multivariate sign tests for heavy-tailed and skewed distributions.