The geometry of the affine invariant multivariate sign and rank methods

Abstract

For k-variate data sets, hyperplanes determined by the k-subsets of observations and the normals of these hyperplanes are discussed. Their use in defining multi-variate invariant concepts of sign and rank and multivariate median (based on the Oja criterion) as well as in the computation of these methods is illustrated.

Keywords:

• Hyperplane
• L ₁ methods
• multivariate median
• multivariate rank test
• multivariate sign test
• robustness