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Correction to: Vector quantile regression and optimal transport, from theory to numerics

Carlier, Guillaume; Chernozhukov, Victor; De Bie, Gwendoline; Galichon, Alfred (2022), Correction to: Vector quantile regression and optimal transport, from theory to numerics, Empirical Economics, 62, 1, p. 63-63. 10.1007/s00181-020-01933-0

Type
Article accepté pour publication ou publié
Date
2022
Journal name
Empirical Economics
Volume
62
Number
1
Publisher
Springer
Pages
63-63
Publication identifier
Metadata
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Author(s)
Carlier, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Chernozhukov, Victor
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Massachusetts Institute of Technology [MIT]
De Bie, Gwendoline
Département de Mathématiques et Applications - ENS Paris [DMA]
Galichon, Alfred cc
Département d'économie (Sciences Po) [ECON]
Abstract (EN)
In this paper, we first revisit the Koenker and Bassett variational approach to (univariate) quantile regression, emphasizing its link with latent factor representations and correlation maximization problems. We then review the multivariate extension due to Carlier et al. (Ann Statist 44(3):1165–92, 2016,; J Multivariate Anal 161:96–102, 2017) which relates vector quantile regression to an optimal transport problem with mean independence constraints. We introduce an entropic regularization of this problem, implement a gradient descent numerical method and illustrate its feasibility on univariate and bivariate examples.
Subjects / Keywords
Vector quantile regression; Optimal transport with mean independence constraints; Latent factors; Entropic regularization