## The Annals of Statistics

### On the efficiency of multivariate spatial sign and rank tests

#### Abstract

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

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

Dates
First available in Project Euclid: 12 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1031833663

Digital Object Identifier
doi:10.1214/aos/1031833663

Mathematical Reviews number (MathSciNet)
MR1439313

Zentralblatt MATH identifier
0873.62048

#### Citation

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. https://projecteuclid.org/euclid.aos/1031833663

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