• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail

Vector Quantile Regression: An optimal transport approach

Carlier, Guillaume; Chernozhukov, Victor; Galichon, Alfred (2016), Vector Quantile Regression: An optimal transport approach, Annals of Statistics, 44, 3, p. 1165-1192. 10.1214/15-AOS1401

View/Open
PaperVQR11Apr2014.pdf (570.0Kb)
Type
Article accepté pour publication ou publié
External document link
https://arxiv.org/abs/1406.4643v4
Date
2016
Journal name
Annals of Statistics
Volume
44
Number
3
Published in
Paris
Pages
1165-1192
Publication identifier
10.1214/15-AOS1401
Metadata
Show full item record
Author(s)
Carlier, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Chernozhukov, Victor

Galichon, Alfred
Abstract (EN)
We propose a notion of conditional vector quantile function and a vectorquantile regression.A conditional vector quantile function (CVQF) of a random vectorY, taking valuesinRdgiven covariatesZ=z, taking values inRp, is a mapu7!QYjZ(u;z), which ismonotone, in the sense of being a gradient of a convex function, and such that given thatvectorUfollows a reference non-atomic distributionFU, for instance uniform distributionon a unit cube inRd, the random vectorQYjZ(U;z) has the conditional distribution ofYconditional onZ=z. Moreover, we have a strong representation,Y=QYjZ(U;Z) almostsurely, for some version ofU.The vector quantile regression (VQR) is a linear model for CVQF ofYgivenZ. Undercorrect speci cation, the notion produces strong representation,Y=(U)>f(Z), forf(Z) denoting a known set of transformations ofZ, whereu7!(u)>f(Z) is a monotonemap, the gradient of a convex function, and the quantile regression coe cientsu7!(u)have the interpretations analogous to that of the standard scalar quantile regression. Asf(Z) becomes a richer class of transformations ofZ, the model becomes nonparametric,as in series modelling. A key property of VQR is the embedding of the classical Monge-Kantorovich's optimal transportation problem at its core as a special case.In the classical case, whereYis scalar, VQR reduces to a version of the classical QR,and CVQF reduces to the scalar conditional quantile function. Several applications todiverse problems such as multiple Engel curve estimation, and measurement of nancialrisk, are considered.
Subjects / Keywords
Brenier; Monge-Kantorovich; vector conditional quantile function; Vector quantile regression
JEL
C21 - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions
C14 - Semiparametric and Nonparametric Methods: General

Related items

Showing items related by title and author.

  • Thumbnail
    Vector quantile regression beyond the specified case 
    Carlier, Guillaume; Chernozhukov, Victor; Galichon, Alfred (2016-10) Article accepté pour publication ou publié
  • Thumbnail
    From Knothe's transport to Brenier's map and a continuation method for optimal transport 
    Santambrogio, Filippo; Carlier, Guillaume; Galichon, Alfred (2010) Article accepté pour publication ou publié
  • Thumbnail
    SISTA : learning optimal transport costs under sparsity constraints 
    Carlier, Guillaume; Dupuy, Arnaud; Galichon, Alfred; Sun, Yifei (2021) Document de travail / Working paper
  • Thumbnail
    Pareto efficiency for the concave order and multivariate comonotonicity 
    Carlier, Guillaume; Dana, Rose-Anne; Galichon, Alfred (2012) Article accepté pour publication ou publié
  • Thumbnail
    Exponential convergence for a convexifying equation 
    Galichon, Alfred; Carlier, Guillaume (2012) Article accepté pour publication ou publié
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo