Wasserstein and weighted metrics for multidimensional Gaussian distributions

M. Y. Kelbert; Y. Suhov

doi:10.18500/1816-9791-2023-23-4-422-434

Wasserstein and weighted metrics for multidimensional Gaussian distributions

M. Y. Kelbert
, Y. Suhov

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	422-434
Number of pages	13
Journal	Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
Volume	23
Issue number	4
DOIs	https://doi.org/10.18500/1816-9791-2023-23-4-422-434
State	Published - 2023

All Science Journal Classification (ASJC) codes

General Computer Science
General Mathematics
Mechanics of Materials
Mechanical Engineering

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10.18500/1816-9791-2023-23-4-422-434

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AB - 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.

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Wasserstein and weighted metrics for multidimensional Gaussian distributions

Abstract

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