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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2023, Volume 23, Issue 4, Pages 422–434
DOI: https://doi.org/10.18500/1816-9791-2023-23-4-422-434 (Mi isu993) 		 
Scientific Part
Mathematics

Wasserstein and weighted metrics for multidimensional Gaussian distributions

M. Y. Kelberta, Y. Suhovb

a Higher School of Economics — National Research University, 20 Myasnitskaya St., Moscow 101000, Russia
b DPMMS, Penn State University, 201 Old Main, State College, PA 16802, USA
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DOI: https://doi.org/10.18500/1816-9791-2023-23-4-422-434
Abstract: We present a number of low and upper bounds for Lévy – Prokhorov, Wasserstein, Frechét, 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: Lévy – Prokhorov distance, Wasserstein distance, weighted total variance distance, Dobrushin's inequality, weighted Pinsker's inequality, weighted le Cam's inequality, weighted Fano's inequality.
Funding agency Grant number
Russian Science Foundation 23-21-00052
HSE Basic Research Program
This research is supported by the Russian Science Fund (project No. 23-21-00052) and the HSE University Basic Research Program.
Received: 09.12.2022
Accepted: 25.12.2022
Bibliographic databases:
Document Type: Article
UDC: 519.85
Language: English
Citation: M. Y. Kelbert, Y. Suhov, “Wasserstein and weighted metrics for multidimensional Gaussian distributions”, Izv. Saratov Univ. Math. Mech. Inform., 23:4 (2023), 422–434
Citation in format AMSBIB
\Bibitem{KelSuk23}
\by M.~Y.~Kelbert, Y.~Suhov
\paper Wasserstein and weighted metrics for multidimensional Gaussian distributions
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2023
\vol 23
\issue 4
\pages 422--434
\mathnet{http://mi.mathnet.ru/isu993}
\crossref{https://doi.org/10.18500/1816-9791-2023-23-4-422-434}
\edn{https://elibrary.ru/ANLRAB}
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