Efficient Fully Distribution-Free Center-Outward Rank Tests for Multiple-Output Regression and MANOVA

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 century. None of the many solutions proposed so far is enjoying combination distribution-freeness and efficiency that makes successful tool in univariate setting. A concept center-outward ranks signs based on measure transportation ideas been introduced recently. Center-outward are not only distribution-free but achieve dimension d > 1 (essential) maximal ancillarity property traditional ranks. In present case, we show fully testing procedures can parametric efficiency. We establish Hájek representation asymptotic normality results required construction tests models. Simulations empirical study demonstrate excellent performance procedures.