Thumbnail - No thumbnail

Vector quantile regression beyond the specified case

Carlier, Guillaume; Chernozhukov, Victor; Galichon, Alfred (2016), Vector quantile regression beyond the specified case, Journal of Multivariate Analysis, 161, p. 96-102. https://doi.org/10.1016/j.jmva.2017.07.003

Type
Article accepté pour publication ou publié
External document link
https://arxiv.org/pdf/1610.06833.pdf
Date
2016-10
Journal name
Journal of Multivariate Analysis
Volume
161
Publisher
Academic Press
Pages
96-102
Publication identifier
Metadata
Show full item record
Author(s)
Carlier, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Chernozhukov, Victor
MIT Department of Economics
Galichon, Alfred
Courant Institute of Mathematical Sciences [New York] [CIMS]
Abstract (EN)
This paper studies vector quantile regression (VQR), which models the dependence of a random vector with respect to a vector of explanatory variables with enough flexibility to capture the whole conditional distribution, and not only the conditional mean. The problem of vector quantile regression is formulated as an optimal transport problem subject to an additional mean-independence condition. This paper provides results on VQR beyond the specified case which had been the focus of previous work. We show that even beyond the specified case, the VQR problem still has a solution which provides a general representation of the conditional dependence between random vectors.
Subjects / Keywords
Duality; Optimal transport; Vector quantile regression