Monge-Kantorovich Depth, Quantiles, Ranks, and Signs
Victor Chernozhukov,
Alfred Galichon,
Marc Hallin and
Marc Henry
Papers from arXiv.org
Abstract:
We propose new concepts of statistical depth, multivariate quantiles, ranks and signs, based on canonical transportation maps between a distribution of interest on $R^d$ and a reference distribution on the $d$-dimensional unit ball. The new depth concept, called Monge-Kantorovich depth, specializes to halfspace depth in the case of spherical distributions, but, for more general distributions, differs from the latter in the ability for its contours to account for non convex features of the distribution of interest. We propose empirical counterparts to the population versions of those Monge-Kantorovich depth contours, quantiles, ranks and signs, and show their consistency by establishing a uniform convergence property for empirical transport maps, which is of independent interest.
Date: 2014-12, Revised 2015-09
References: View references in EconPapers View complete reference list from CitEc
Citations:
Downloads: (external link)
http://arxiv.org/pdf/1412.8434 Latest version (application/pdf)
Related works:
Working Paper: Monge-Kantorovich Depth, Quantiles, Ranks, and Signs (2017) 
Working Paper: Monge-Kantorovich Depth, Quantiles, Ranks, and Signs (2017) 
Working Paper: Monge-Kantorovich depth, quantiles, ranks and signs (2015) 
Working Paper: Monge-Kantorovich depth, quantiles, ranks and signs (2015) 
Working Paper: Monge-Kantorovich Depth, Quantiles, Ranks and Signs (2015) 
Working Paper: Monge-Kantorovich Depth, Quantiles, Ranks, and Signs (2015) 
Working Paper: Monge-Kantorovich Depth, Quantiles, Ranks, and Signs (2015) 
Working Paper: Monge-Kantorovich depth, quantiles, ranks and signs (2015) 
Working Paper: Monge-Kantorovich depth, quantiles, ranks and signs (2015) 
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:arx:papers:1412.8434
Access Statistics for this paper
More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().