The Annals of Statistics

On the efficiency of multivariate spatial sign and rank tests

Jyrki Möttönen, Hannu Oja, and Juha Tienari

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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.

Article information

Ann. Statist., Volume 25, Number 2 (1997), 542-552.

First available in Project Euclid: 12 September 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G10: Hypothesis testing 62G20: Asymptotic properties 62H15: Hypothesis testing
Secondary: 62H11: Directional data; spatial statistics

Angle test asymptotic efficiency multivariate location multivariate rank test multivariate sign test spatial median


Möttönen, Jyrki; Oja, Hannu; Tienari, Juha. On the efficiency of multivariate spatial sign and rank tests. Ann. Statist. 25 (1997), no. 2, 542--552. doi:10.1214/aos/1031833663.

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