Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Kelbert M. Y., Suhov Y. M. Wasserstein and weighted metrics for multidimensional Gaussian distributions. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2023, vol. 23, iss. 4, pp. 422-434. DOI: 10.18500/1816-9791-2023-23-4-422-434, EDN: ANLRAB

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
30.11.2023
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Language: 
English
Heading: 
Mathematics
Article type: 
Article
UDC: 
519.85
DOI: 
10.18500/1816-9791-2023-23-4-422-434
EDN: 
ANLRAB

Wasserstein and weighted metrics for multidimensional Gaussian distributions

Autors: 
Kelbert Mark Yakovlevich, Higher School of Economics – National Research University
Suhov Yurii M., DPMMS, Penn State University
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. 

Key words: 
Levy – Prokhorov distance
Wasserstein distance
Weighted Total Variance Distance
Dobrushin’s inequality
weighted Pinsker’s inequality
weighted le Cam’s inequality
weighted Fano’s inequality
Acknowledgments: 
This research is supported by the Russian Science Fund (project No. 23-21-00052) and the HSE University Basic Research Program.
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Received: 
09.12.2022
Accepted: 
25.12.2022
Published: 
30.11.2023
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