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Parseval’s identity and optimal transport maps

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  • Ghaffari, N.
  • Walker, S.G.

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.

Suggested Citation

  • Ghaffari, N. & Walker, S.G., 2021. "Parseval’s identity and optimal transport maps," Statistics & Probability Letters, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:stapro:v:170:y:2021:i:c:s0167715220302923
    DOI: 10.1016/j.spl.2020.108989
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    References listed on IDEAS

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    1. Alfonsi, A. & Jourdain, B., 2014. "A remark on the optimal transport between two probability measures sharing the same copula," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 131-134.
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    Cited by:

    1. Ghaffari, N. & Walker, S.G., 2023. "W2 barycenters for radially related distributions," Statistics & Probability Letters, Elsevier, vol. 195(C).

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