A Quantitative Cram\'er-Wold Theorem for Zolotarev Distances

TL;DR

This paper presents a quantitative version of the Cramér-Wold theorem, providing an upper bound for Zolotarev distances between high-dimensional probability measures based on their one-dimensional projections.

Contribution

It introduces a new bound connecting multidimensional Zolotarev distances to one-dimensional projections, advancing the understanding of measure similarity in high dimensions.

Findings

Derived an explicit upper bound for Zolotarev distances

Connected high-dimensional distances to one-dimensional projections

Enhanced tools for analyzing probability measures in Euclidean spaces

Abstract

An upper bound for Zolotarev distances between probability measures on multidimensional Euclidean spaces is given in terms of similar distances between one dimensional projections.