This was part of Applied Optimal Transport
Nonparametric Multiple-Output Center-Outward Quantile Regression
Eustasio del Barrio, Universidad de Valladolid
Friday, May 20, 2022
Abstract: This talk addresses the problem of non parametric multiple-output quantile regression based on the novel concept of multivariate center-outwardquantiles introduced in Chernozhukov et al. (2017) and Hallin et al. (2021). To obtain conditional quantile regions and contours, the conditional center-outward quantiles are defined. A new cyclically monotone interpolation, with non-necessarily constant weights, is proposed to define them. This method is completely non-parametric and produces interpretable empirical regions/contours which converge in probability to its population counterpart. The presentation will include with some real and synthetic examples, showing the adaptation and applicability of the method, in particular its ability to catch the heteroskedasticity and the trend of the data.