eprintid: 16726
rev_number: 11
eprint_status: archive
userid: 1482
importid: 105
dir: disk0/00/01/67/26
datestamp: 2015-03-16 14:56:38
lastmod: 2021-10-27 13:36:42
status_changed: 2016-04-19 13:51:32
type: article
metadata_visibility: show
creators_name: Faugeras, Olivier
creators_idrefppn: 033404054
creators_affiliation: Toulouse School of Economics - GREMAQ
title: Maximal coupling of empirical copulas for discrete vectors
ispublished: pub
subjects: subjects_ECO
abstract: For a vector View the MathML source with a purely discrete multivariate distribution, we give simple short proofs of uniform a.s. convergence on their whole domain of two versions of genuine empirical copula functions, obtained either via probabilistic continuation, i.e. kernel smoothing, or via the distributional transform. These results give a positive answer to some delicate issues related to the convergence of copula functions in the discrete case. They are obtained under the very weak hypothesis of ergodicity of the sample, a framework which encompasses most types of serial dependence encountered in practice. Moreover, they allow to derive, as simple corollaries, almost sure consistency results for some recent extensions of concordance measures attached to discrete vectors. The proofs are based on a maximal coupling construction of the empirical cdf, a result of independent interest.
date: 2015-05
date_type: published
publisher: Elsevier
id_number: 10.1016/j.jmva.2015.02.013
official_url: http://tse-fr.eu/pub/29123
faculty: tse
divisions: tse
keywords: Discrete vector
keywords: Maximal coupling
keywords: a
keywords: s
keywords: constructions
keywords: Empirical copula
keywords: Ergodicity
language: en
has_fulltext: FALSE
doi: 10.1016/j.jmva.2015.02.013
view_date_year: 2015
full_text_status: none
publication: Journal of Multivariate Analysis
volume: vol.137
pagerange: 179-186
refereed: TRUE
issn: 0047-259X
oai_identifier: oai:tse-fr.eu:29123
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oai_lastmod: 2015-11-10T17:10:50Z
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oai_set: ut1c
site: ut1
citation:   Faugeras, Olivier <https://www.idref.fr/033404054>  (2015) Maximal coupling of empirical copulas for discrete vectors.    Journal of Multivariate Analysis, vol.137.  pp. 179-186.