Vector quantile regression and optimal transport, from theory to numerics

Guillaume Carlier (), Victor Chernozhukov, Gwendoline De Bie () and Alfred Galichon ()
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Guillaume Carlier: Université Paris IX Dauphine
Gwendoline De Bie: DMA, ENS
Alfred Galichon: New York University

Empirical Economics, 2022, vol. 62, issue 1, No 3, 35-62

Abstract: Abstract 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.

Keywords: Vector quantile regression; Optimal transport with mean independence constraints; Latent factors; Entropic regularization (search for similar items in EconPapers)
JEL-codes: C51 C60 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00181-020-01919-y

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