## 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.

### MSC:

 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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### References:

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