Parseval’s identity and optimal transport maps

N. Ghaffari and S.G. Walker

Statistics & Probability Letters, 2021, vol. 170, issue C

Abstract: Recent findings for optimal transport maps between distribution functions sharing the same copula show that componentwise the solution is the optimal map between the 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.

Keywords: Positive definite matrix; Orthonormal matrix; Copula; Optimal transportation; Convex function; Barycenter (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2020.108989

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