An Affine Invariant Bivariate Version of the Sign Test

SUMMARY The generalized median of Oja yields a notion of bivariate quantile and, in turn, an affine invariant bivariate analogue of the sign test. its properties include a simple null covariance formula, facilitating a permutation or sign change test in the case of bivariate symmetry, normal efficiency coinciding with that of the Oja median and bounded influence, and hence strong robustness.