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W2 barycenters for radially related distributions

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  • Ghaffari, N.
  • Walker, S.G.

Abstract

This note details the Wasserstein-2 Barycenter for distributions which are spherically equivalent. Separating random variables which have spherically equivalent distributions are the radial component distributions. We show the Barycenter corresponds to a quantile averaging of the distributions. An illustration involving Student-t distributions is presented.

Suggested Citation

  • Ghaffari, N. & Walker, S.G., 2023. "W2 barycenters for radially related distributions," Statistics & Probability Letters, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:stapro:v:195:y:2023:i:c:s0167715223000123
    DOI: 10.1016/j.spl.2023.109788
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    1. Eckhard Platen & Renata Rendek, 2007. "Empirical Evidence on Student-t Log-Returns of Diversified World Stock Indices," Research Paper Series 194, Quantitative Finance Research Centre, University of Technology, Sydney.
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    3. Markowitz, Harry M & Usmen, Nilufer, 1996. "The Likelihood of Various Stock Market Return Distributions, Part 2: Empirical Results," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 221-247, November.
    4. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    5. Ghaffari, N. & Walker, S.G., 2021. "Parseval’s identity and optimal transport maps," Statistics & Probability Letters, Elsevier, vol. 170(C).
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