A Prelude to Statistics in Wasserstein Metric Spaces

Abstract

Purpose – This paper aims mainly at introducing applied statisticians and econometricians to the current research methodology with non-Euclidean data sets. Specifically, it provides the basis and rationale for statistics in Wasserstein space, where the metric on probability measures is taken as a Wasserstein metric arising from optimal transport theory.
Design/methodology/approach – The authors spell out the basis and rationale for using Wasserstein metrics on the data space of (random) probability measures.
Findings – In elaborating the new statistical analysis of non-Euclidean data sets, the paper illustrates the generalization of traditional aspects of statistical inference following Frechet's program.
Originality/value – Besides the elaboration of research methodology for a new data analysis, the paper discusses the applications of Wasserstein metrics to the robustness of financial risk measures.