Abstract
Every multivariate sign and rank test needs a workable concept of ranks for multivariate data. Unfortunately, multidimensional spaces lack natural ordering and, consequently, there are no universally accepted ways how to rank vector observations.
Existing proposals usable beyond small dimensions are very few in number, and each of them has its own advantages and drawbacks. Therefore, new multivariate ranks based on randomized lift-interdirections are presented, discussed and investigated.
These naturally robust and invariant hyperplane-based ranks can be computed quickly and easily even in relatively high-dimensional spaces, and they can be used for nonparametric statistical inference in some existing optimal statistical procedures without altering their asymptotic behavior under null hypotheses or changing their performance under local alternatives. This is not only proved theoretically in case of the canonical sign and rank one-sample test for elliptically distributed observations, but also illustrated empirically in a small simulation study. (C) 2022 Elsevier B.V.
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