A prelude to statistics in Wasserstein metric spaces

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.