2022/04/25 by del Barrio, Eustasio, Sanz, Alberto Gonzalez, Hallin, Marc · 4 citations
#FOS: Computer and information sciences #FOS: Mathematics #G.3 #Methodology (stat.ME) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2204.11756
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.