Abstract
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.
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Acknowledgements
This work was performed during the PhD of A. Decurninge supported by the DGA/MRIS and Thales.
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© 2015 Springer International Publishing Switzerland
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Decurninge, A. (2015). Multivariate L-Moments Based on Transports. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_13
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DOI: https://doi.org/10.1007/978-3-319-25040-3_13
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