A0306
Title: Nonparametric multiple-output center-outward quantile regression
Authors: Marc Hallin - Universite Libre de Bruxelles (Belgium)
Eustasio del Barrio - Universidad de Valladolid (Spain)
Alberto Gonzalez Sanz - Columbia University (United States) [presenting]
Abstract: Based on the novel concept of multivariate center-outward quantiles, the problem of nonparametric multiple-output quantile regression is considered. The 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 that 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.
