Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

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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

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Wasserstein and weighted metrics for multidimensional Gaussian distributions

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

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. 

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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