Multivariate Quantiles: Geometric and Measure-Transportation-Based Contours

Marc Hallin and Dimitri Konen

No 2023-14, Working Papers ECARES from ULB -- Universite Libre de Bruxelles

Abstract: Quantiles are a fundamental concept in probability and theoretical statistics and a daily tool in their applications. While the univariate concept of quantiles is quite clear and well understood, its multivariate extension is more problematic. After half a century of continued efforts and many proposals, two concepts, essentially, are emerging: the so-called (relabeled) geometric quantiles, extending the characterization of univariate quantiles as minimizers of an L1 loss function involving the check functions, and the more recent center-outward quantiles based on measuretransportation ideas. These two concepts yield distinct families of quantile regions and quantile contours. Our objective here is to present a comparison of their main theoretical properties and a numerical investigation of their differences.

Keywords: multivariate quantiles; geometric quantiles; measure transportation (search for similar items in EconPapers)
Pages: 18 p.
Date: 2023-10
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published by:

Downloads: (external link)
https://dipot.ulb.ac.be/dspace/bitstream/2013/3643 ... NEN-multivariate.pdf Œuvre complète ou partie de l'œuvre (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eca:wpaper:2013/364357

Ordering information: This working paper can be ordered from
http://hdl.handle.ne ... lb.ac.be:2013/364357

Access Statistics for this paper

More papers in Working Papers ECARES from ULB -- Universite Libre de Bruxelles Contact information at EDIRC.
Bibliographic data for series maintained by Benoit Pauwels ().