Arbeitspapier

Monge-Kantorovich depth, quantiles, ranks and signs

to related objects

We propose new concepts of statistical depth, multivariate quantiles, ranks and signs, based on canonical transportation maps between a distribution of interest on IRd 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 elliptical 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.

Language: Englisch

Bibliographic citation: Series: cemmap working paper ; No. CWP04/15

Classification: Wirtschaft

Subject: Statistical depth
vector quantiles
vector ranks
multivariate signs
empirical transport maps
uniform convergence of empirical transport

Event: Geistige Schöpfung

(who): Chernozhukov, Victor
Galichon, Alfred
Hallin, Marc
Henry, Marc

Event: Veröffentlichung

(who): Centre for Microdata Methods and Practice (cemmap)

(where): London

(when): 2015

DOI: doi:10.1920/wp.cem.2015.0415

Handle: http://hdl.handle.net/10419/130021

Last update: 10.03.2025, 11:43 AM CET

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Object type

Arbeitspapier

Associated

Chernozhukov, Victor
Galichon, Alfred
Hallin, Marc
Henry, Marc
Centre for Microdata Methods and Practice (cemmap)

Time of origin

2015

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