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A simpler, affine-invariant, multivariate, distribution-free sign test. (English) Zbl 1009.62047

Summary: A simpler multivariate sign test is proposed that uses the transformation-retransformation approach of B. Chakraborty, P. Chaudhuri and H. Oja [Stat. Sin. 8, No. 3, 767-784 (1998; Zbl 0915.62051)] together with a directional transformation due to D.E. Tyler [Ann. Stat. 15, 234-251 (1987; Zbl 0628.62053)]. 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.

MSC:

62H15 Hypothesis testing in multivariate analysis
62G10 Nonparametric hypothesis testing
62H11 Directional data; spatial statistics

Keywords:

direction test
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