Fully Distribution-free Center-outward Rank Tests for Multiple-output Regression and Manova

Marc Hallin, Daniel Hlubinka and Sarka Hudecova

No 2020-32, Working Papers ECARES from ULB -- Universite Libre de Bruxelles

Abstract: 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 Hájek 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.

Keywords: Multivariate ranks; Multivariate signs; Multiple output regression; MANOVA; MANOVA; Rank test; Hájek representation (search for similar items in EconPapers)
Pages: 31 p.
Date: 2020-07
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (2)

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