A0394
Title: Shift-dispersion decompositions of Wasserstein and Cramer distances
Authors: Johannes Resin - Goethe University Frankfurt (Germany) [presenting]
Timo Dimitriadis - Heidelberg University (Germany)
Johannes Bracher - Karlsruhe Institute of Technology (Germany)
Daniel Wolffram - Karlsruhe Institute of Technology (Germany)
Abstract: Divergence functions are measures of distance or dissimilarity between probability distributions that serve various purposes in statistics and applications. Decompositions of Wasserstein and Cramer distances are proposed, which compare two distributions by integrating over their differences in distribution or quantile functions, into directed shift and dispersion components. These components are obtained by dividing the differences between the quantile functions into contributions arising from shift and dispersion, respectively. The decompositions add information on how the distributions differ in a condensed form and consequently enhance the interpretability of the underlying divergences. It is shown that the decompositions satisfy a number of natural properties and are unique in doing so in location-scale families. The decompositions allow deriving sensitivities of the divergence measures to changes in location and dispersion, and they give rise to weak stochastic order relations that are linked to the usual stochastic and dispersive order. The theoretical developments are illustrated in two applications, where the focus is on forecast evaluation of temperature extremes and on the design of probabilistic surveys in economics.
