Affine Invariant Multivariate One-Sample Sign Tests
提出一种仿射不变的多元符号检验方法，适用于椭圆分布，与Randles检验渐近等价，并给出相对于Hotelling检验的效率下界。
SUMMARY 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.