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

arXiv: https://arxiv.org/abs/2007.15496 · HTML: https://mlsanity.com/paper/2007.15496/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jul 2020.

## Built on by (most cited first, 3 of 3)

- [Multivariate Conformal Prediction using Optimal Transport](https://mlsanity.com/paper/2502.03609/) (2025)
- [Lower Complexity Adaptation for Empirical Entropic Optimal Transport](https://mlsanity.com/paper/2306.13580/) (2023)
- [A New Perspective On Denoising Based On Optimal Transport](https://mlsanity.com/paper/2312.08135/) (2023)

## Abstract (arXiv)

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. We derive here the H'ajek representation and asymptotic normality results required in the construction of center-outward rank tests for multiple-output regression and MANOVA. When based on appropriate spherical scores, these fully distribution-free tests achieve parametric efficiency in the corresponding models.