Fully distribution-free center-outward rank tests for multiple-output regression and MANOVA

Understand

Extending rank-based inference to a multivariate setting such as multiple-output regression or MANOVA with unspecified d-dimensional error density has remained an open problem for more than half a century.

• None of the many solutions proposed so far is enjoying the combination of distribution-freeness and efficiency that makes rank-based inference a successful tool in the univariate setting.
• A concept of center-outward multivariate ranks and signs based on measure transportation ideas has been introduced recently.
• Center-outward ranks and signs are not only distribution-free but achieve in dimension d > 1 the (essential) maximal ancillarity property of traditional univariate ranks, hence carry all the "distribution-free information" available in the sample.