Wasserstein and weighted metrics for multidimensional Gaussian distributions
- Authors: Kelbert M.Y.1, Suhov Y.M.2,3
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Affiliations:
- Higher School of Economics – National Research University
- DPMMS, Penn State University
- University of Cambridge
- Issue: Vol 23, No 4 (2023)
- Pages: 422-434
- Section: Articles
- URL: https://journals.rcsi.science/1816-9791/article/view/250858
- DOI: https://doi.org/10.18500/1816-9791-2023-23-4-422-434
- EDN: https://elibrary.ru/ANLRAB
- ID: 250858
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Abstract
We present a number of low and upper bounds for Levy – Prokhorov, Wasserstein, Frechet, and Hellinger distances between probability distributions of the same or different dimensions. The weighted (or context-sensitive) total variance and Hellinger distances are introduced. The upper and low bounds for these weighted metrics are proved. The low bounds for the minimum of different errors in sensitive hypothesis testing are proved.
About the authors
Mark Yakovlevich Kelbert
Higher School of Economics – National Research University
ORCID iD: 0000-0002-3952-2012
Scopus Author ID: 55884702600
20 Myasnitskaya St., Moscow 101000, Russia
Yurii M. Suhov
DPMMS, Penn State University; University of Cambridge
Scopus Author ID: 35582648200
201 Old Main, State College, PA 16802, USA
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