2018/01/10 by Novin Ghaffari, Ghaffari, Novin, Stephen Walker +1
Mathematics · #60E05 #60E15 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60E05 #msc:60E15
paper · pdf · doi:10.48550/arxiv.1801.03516
15 pages. A correction to "On Multivariate Optimal Transportation
arxiv created 2020/07/13 · arxiv updated 2020/07/15
Recent findings for optimal transport maps between distribution functions sharing the same copula show that componentwise the solution is the optimal map between marginal distributions. This is an important discovery since in the multivariate setting optimal maps are difficult to find and only known in a few special cases. In this paper, we extend the result on common copulas by showing that orthonormal transformations of variables sharing a common copula also have a known optimal map. We illustrate this by establishing optimal maps between members of a class of scale mixture of normal distributions.