B1616
Title: Nonparametric measure-transportation-based multiple-output quantile regression
Authors: Eustasio del Barrio - Universidad de Valladolid (Spain) [presenting]
Alberto Gonzalez-Sanz - University of Columbia (United States)
Marc Hallin - Universite Libre de Bruxelles (Belgium)
Abstract: Based on recent measure-transportation-based concepts of multivariate quantiles, the problem of nonparametric multiple-output quantile regression is considered. The approach defines nested conditional centre-outward quantile regression contours and regions with given conditional probability content, the graphs of which constitute nested centre-outward quantile regression tubes with given unconditional probability content; these (conditional and unconditional) probability contents do not depend on the underlying distribution essential property of quantile concepts. Empirical counterparts of these concepts are constructed, yielding interpretable empirical contours, regions, and tubes, which are shown to consistently reconstruct (in the Pompeiu-Hausdorff topology) their population versions. The method is non-parametric and performs well in simulations- possibly with heteroskedasticity and nonlinear trends. Its potential as a data-analytic tool is illustrated on some real datasets.
