Seminar: Nonparametric Multiple-Output Center-Outward Quantile Regression

Professor Marc Hallin, Université Libre de Bruxelles, Belgium, will give a joint departmental seminar together with the department of Statistics. 

Abstract:  Building on recent 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 (conditional and unconditional) probability contents do not depend on the underlying distribution---an 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. Our method is entirely non-parametric and performs well in simulations---with possible heteroskedasticity and nonlinear trends. Its potential as a data-analytic tool is illustrated on some real datasets.

-----------------------------------------------------------------

Marc’s research covers a broad spectrum of fundamental and applied statistical topics, including statistical decision, time series, random fields, density estimation, multivariate analysis, panel data, inequalities, high-dimensional and “big data” problems, quantile regression, spectral analysis, data depth, the asymptotic theory of statistical experiments, statistical applications of measure transportation, and econometrics.  

He is currently an Associate Editor of, among others: Journal of the American Statistical Association (JASA), Journal of Business and Economics Statistics (JBES), Statistical Inference for Stochastic Processes, Statistical Methods and Applications.

You can find more details here:

https://ecares.ulb.be/wp-content/uploads/2022/11/CVMHallin2022.pdf

and a commented bibliography here:

https://ecares.ulb.be/wp-content/uploads/2021/01/MH_CommentedBibliography_2020.pdf