AFFINE INVARIANT MULTIVARIATE ONE-SAMPLE SIGN TESTS

Brown and Hettmansperger introduced an affine invariant bivariate anal ogue of the sign test based on the generalized median of Oja. In this paper its general multivariate extension is presented. The proposed mu ltivariate permutation or sign change test is affine invariant with an easily computable covariance matrix. For elliptic distributions the p roposed test and Randles's test are asymptotically equivalent. Formula e for calculating asymptotic relative efficiencies of the proposed tes t and the Oja multivariate median are given. Lower bounds for the effi ciencies of the new test (and the Randles test) relative to the classi cal Hotelling test are established for elliptic alternatives and for u nimodal elliptic alternatives. Relative efficiencies under multivariat e t-distributions are also tabulated. The theory is illustrated by a s imple example.