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Abstract 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. Key Words: Direction testNonparametric
Ronald H. Randles (Fri,) studied this question.