Lecture of Prof. Marc Hallin at the University of Wrocław
Within IDUB’s program – short visits – a lecture by Professor Marc Hallin of the Université Libre de Bruxelles, titled “The long quest for quantiles and ranks in Euclidean spaces and on manifolds,” will take place. The event will take place at 13:15 on Tuesday, June 17th, 2024, in lecture room 119 of the Institute of Computer Science at the University of Wrocław, ul. Joliot-Curie 15.
The meeting is held within the framework of the pro-quality activities implemented in the Excellence Initiative – Research Universityproject.
All interested parties are warmly invited.
Abstract
Quantiles are a fundamental concept in probability and a crucial tool in statistics, spanning both descriptive and inferential methods. However, despite decades of effort, there is still no fully satisfactory and universally accepted definition of quantiles—or their dual notion, ranks—beyond the well-understood univariate setting. This gap is particularly pressing for multivariate variables in Euclidean spaces, directional data on hyperspheres, and more generally, variables that take values on manifolds. Unlike the real line, these domains lack a natural ordering.
We show that measure transportation can address this challenge by providing a way to define orderings and quantile functions that depend on the underlying distribution (or on the data, in the empirical case). These center-outward distribution and quantile functions—corresponding to ranks and signs in the empirical case—satisfy all the properties expected of such concepts and reduce, in the case of real-valued variables, to the classical univariate definitions.
Bio
Professor Hallin, a prominent expert in time series analysis, econometrics, and nonparametric inference, is an author or co-author of more than 250 scientific articles for which he has received numerous awards. Among them are the medal of the Faculty of Mathematics and Physics at Charles University in Prague (2006), the Humboldt Prize awarded by the Alexander von Humboldt Foundation (2012), the Pierre-Simon de Laplace Prize awarded by the French Statistical Society (2022), and the Gottfried E. Noether Prize for Outstanding Scientist awarded by the American Statistical Society (2022).
He has delivered many prestigious lectures, including the Hermann Otto Hirschfeld Lecture Series at Humboldt University of Berlin in 2017 and the Mahalanobis Memorial Lecture at the Indian Statistical Institute in 2018.
Over the years, he has co-edited more than a dozen books and conference volumes. He has been a part of the editorial boards of many journals, including the Journal of Time Series Analysis (1994–2009), Journal of Econometrics (2013–2019), Journal of Business and Economic Statistics (od 2018), and section Theory and Methods of Journal of the American Statistical Association (od 2005).
He is a member (Fellow) of the Institute of Mathematical Statistics (1990), the American Statistical Association (1997), and the Class of Sciences (Classe des Sciences) of the Royal Belgian Academy (1999).
Translated by Jakub Wolf (student of English Studies at the University of Wrocław) as part of the translation practice.
Date of publication: 11.06.2025
Added by: M.K.
