On the efficiency of multivariate spatial sign and rank tests. (English) Zbl 0873.62048

Summary: Asymptotic Pitman efficiencies of multivariate spatial sign and rank methods are considered in the one-sample location case. Limiting distributions of the spatial sign and signed-rank tests under the null hypothesis as well as under contiguous sequences of alternatives are given. Formulae for asymptotic relative efficiencies are found and, under multivariate \(t\) distributions, relative efficiencies with respect to Hotelling’s \(T^2\) test are calculated.


62G10 Nonparametric hypothesis testing
62H15 Hypothesis testing in multivariate analysis
62G20 Asymptotic properties of nonparametric inference
62H11 Directional data; spatial statistics
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