Multivariate L-Moments Based on Transports
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.
KeywordsOrthogonal Basis Quantile Function Optimal Transport Conditional Quantile Multivariate Extension
This work was performed during the PhD of A. Decurninge supported by the DGA/MRIS and Thales.
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