Vector quantile regression beyond the specified case

Guillaume Carlier, Victor Chernozhukov, Alfred Galichon

    Research output: Contribution to journalArticlepeer-review


    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.

    Original languageEnglish (US)
    Pages (from-to)96-102
    Number of pages7
    JournalJournal of Multivariate Analysis
    StatePublished - Sep 2017


    • Duality
    • Optimal transport
    • Vector quantile regression

    ASJC Scopus subject areas

    • Statistics and Probability
    • Numerical Analysis
    • Statistics, Probability and Uncertainty


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