Affine Invariant Multivariate One-Sample Sign Tests

Brown and Hettmansperger introduced an affine invariant bivariate analogue of the sign test based on the generalized median of Oja. In this paper its general multivariate extension is presented. The proposed multivariate permutation or sign change test is affine invariant with an easily computable c...

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Veröffentlicht in:Journal of the Royal Statistical Society. Series B, Methodological Methodological, 1994-01, Vol.56 (1), p.221-234
Hauptverfasser: Hettmansperger, Thomas P., Nyblom, Jukka, Oja, Hannu
Format: Artikel
Sprache:eng
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Zusammenfassung:Brown and Hettmansperger introduced an affine invariant bivariate analogue of the sign test based on the generalized median of Oja. In this paper its general multivariate extension is presented. The proposed multivariate permutation or sign change test is affine invariant with an easily computable covariance matrix. For elliptic distributions the proposed test and Randles's test are asymptotically equivalent. Formulae for calculating asymptotic relative efficiencies of the proposed test and the Oja multivariate median are given. Lower bounds for the efficiencies of the new test (and the Randles test) relative to the classical Hotelling test are established for elliptic alternatives and for unimodal elliptic alternatives. Relative efficiencies under multivariate t-distributions are also tabulated. The theory is illustrated by a simple example.
ISSN:0035-9246
1369-7412
2517-6161
1467-9868
DOI:10.1111/j.2517-6161.1994.tb01973.x