2021/02/25 by Guillaume Carlier, Victor Chernozhukov, Gwendoline De Bie +1
Economics, Econometrics and Finance · #econ.GN #q-fin.EC
paper · pdf · doi:10.1007/s00181-020-01919-y
published as Empirical Economics (2020) · 35 pages, 19 figures, 4 tables. arXiv admin note: text overlap with arXiv:1610.06833
arxiv created 2021/02/25 · arxiv updated 2021/02/26
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. (2016, 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.