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Volume 8 - Number 1 | March 2024

A prelude to statistics in Wasserstein metric spaces

Chon Van Le, and Uyen Hoang Pham

25/03/2024 12 0 0
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Frechet mean sets Histogram data sets Optimal transport Random probability measures Robustness of financial risk measures Wasserstein metrics Wasserstein sampling spaces WGAN

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.

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JEL classification: C10

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