Multivariate L-Moments Based on Transports

  • Alexis DecurningeEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9389)


Univariate L-moments are expressed as projections of the quantile function onto an orthogonal basis of univariate polynomials. We present multivariate versions of L-moments expressed as collections of orthogonal projections of a multivariate quantile function on a basis of multivariate polynomials. We propose to consider quantile functions defined as transports from the uniform distribution on \([0;1]^d\) onto the distribution of interest and present some properties of the subsequent L-moments. The properties of estimated L-moments are illustrated for heavy-tailed distributions.


Orthogonal Basis Quantile Function Optimal Transport Conditional Quantile Multivariate Extension 
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This work was performed during the PhD of A. Decurninge supported by the DGA/MRIS and Thales.


  1. 1.
    Aurenhammer, F.: Power diagrams: properties, algorithms and applications. SIAM J. Comput. 16(1), 78–96 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Decurninge, A.: Multivariate quantiles and multivariate L-moments. arXiv:1409.6013 (2014)
  3. 3.
    Decurninge, A.: Univariate and multivariate quantiles, probabilistic and statistical approaches; radar applications. Ph.D. Dissertation (2015)Google Scholar
  4. 4.
    Galichon, A., Henry, M.: Dual theory of choice with multivariate risks. J. Econ. Theor. 147(4), 1501–1516 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Gu, X., Luo, F., Sun, J., Yau, S.-T.: Variational principles for Minkowski type problems, discrete optimal transport, and discrete Monge-Ampere equations. arXiv:1302.5472 (2013)
  6. 6.
    Hosking, J.R.: L-moments: analysis and estimation of distributions using linear combinations of order statistics. J. Roy. Stat. Soc. 52(1), 105–124 (1990)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Villani, C.: Topics in optimal transportation. In: Graduate Studies in Mathematics, vol. 58. American Mathematical Society (2003)Google Scholar
  8. 8.
    Serfling, R., Xiao, P.: A contribution to multivariate L-moments: L-comoment matrices. J. Multivariate Anal. 98(9), 1765–1781 (2007)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Mathematical and Algorithmic Sciences Lab, France Research CenterHuawei Technologies Co. Ltd.Boulogne-BillancourtFrance

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