Multivariate spatial sign and rank methods

Abstract

Rotation invariant multivariate spatial sign and rank tests and corresponding rotation equivariant estimates based on L1 type objective function with Euclidean distance are considered. Multivariate spatial analogues of sign and rank concepts, one- and two-sample sign tests, Wilcoxon rank sum and signed rank tests, median and Hodges-Lehmann estimates are reviewed and discussed. Connections with other generalization are considered. The testing theory is illustrated by two examples.