Incomplete interdirections and lift-interdirections

摘要

The article presents, discusses, and explores incomplete variants of interdirections, lift-interdirections, and symmetrised lift-interdirections (with a few incomplete designs). Although they are easier to compute in high-dimensional spaces than the originals, they can still replace them in many optimal statistical procedures based on signs and ranks without significantly changing their properties. This is proved theoretically and confirmed empirically in a small simulation study dealing with the canonical examples of multivariate sign and signed-rank one-sample tests applied to high-dimensional data sets.