Nonparametric Multiple-Output Center-Outward Quantile Regression

Eustasio del Barrio, Alberto González-Sanz and Marc Hallin

No 2022-10, Working Papers ECARES from ULB -- Universite Libre de Bruxelles

Abstract: Based on the novel concept of multivariate center-outward quantiles introduced recently in Chernozhukov et al. (2017) and Hallin et al. (2021), we are considering the problem of nonparametric multiple-output quantile regression. Our approach defines nested conditional center-outward quantile regression contours and regions with given conditional probability content irrespective of the underlying distribution; their graphs constitute nested center-outward quantile regression tubes. Empirical counterparts of these concepts are constructed, yielding interpretable empirical regions andcontours which are shown to consistently reconstruct their population versions in the Pompeiu-Hausdorff topology. Our method is entirely non-parametric and performs well in simulations including heteroskedasticity and nonlinear trends; its power as a data-analytic tool is illustrated on some real datasets.

Keywords: Multiple-output regression; Center-outward quantiles; Optimal transport (search for similar items in EconPapers)
Pages: 36 p.
Date: 2022-05
New Economics Papers: this item is included in nep-ecm and nep-eff
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Citations: View citations in EconPapers (7)

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