Multivariate quantiles and multivariate L-moments

2014/09/21 by Decurninge, Alexis
#FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1409.6013

Abstract

Univariate L-moments are expressed as projections of the quantile function onto an orthogonal basis of polynomials in L₂([0;1],ℝ). We present multivariate versions of L-moments expressed as collections of orthogonal projections of a multivariate quantile function on a basis of multivariate polynomials in L₂([0;1]^d,ℝ). We propose to consider quantile functions defined as transport from the uniform distribution on [0;1]^d onto the distribution of interest. In particular, we present the quantiles defined by the transport of Rosenblatt and the optimal transport and the properties of the subsequent L-moments.

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