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arXiv · 2204.11756

Nonparametric Multiple-Output Center-Outward Quantile Regression

Eustasio del Barrio·Alberto Gonzalez Sanz·Marc Hallin
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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 and contours 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.

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Eustasio del Barrio, Alberto Gonzalez Sanz, Marc Hallin. 2022-04-25. Nonparametric Multiple-Output Center-Outward Quantile Regression. https://arxiv.org/abs/2204.11756

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