Statistics and Data Science Seminar: Nonparametric Multiple-Output Center-Outward Quantile Regression

Co-sponsored by TRIADS

Abstract: Based on novel measure-transportation-based concepts of multivariate quantiles, 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 the graphs of which constitute nested center-outward quantile regression ''tubes'' with given unconditional probability content; these probability contents do not depend on the underlying distribution. 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. Our method is entirely 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. *Based on joint work with Eustasio del Barrio and Alberto Gonzalez Sanz.

Bio: Marc Hallin is Professor Emeritus at the Université libre de Bruxelles. He is an Elected member of the International Statistical Institute, Fellow of the Institute of Mathematical Statistics and of the American Statistical Association, Member of the Classe des Sciences of the Royal Academy of Belgium. He has received several distinctions, including the Pierre-Simon de Laplace Prize, the highest scientific distinction awarded by the French Statistical Society, and the Noether Distinguished Scholar Award from the American Statistical Association. His research interests are in mathematical statistics, particularly semiparametric and rank-based inference, statistical depth, quantile-oriented models, and measure transportation. He has also made significant contributions in time series and time series econometrics, with special focus on factor models in the analysis of high-dimensional time series.

Host: Debashis Mondal