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New Upper Bounds in the Hypothesis Testing Problem with Information Constraints

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Abstract

We consider a hypothesis testing problem where a part of data cannot be observed. Our helper observes the missed data and can send us a limited amount of information about them. What kind of this limited information will allow us to make the best statistical inference? In particular, what is the minimum information sufficient to obtain the same results as if we directly observed all the data? We derive estimates for this minimum information and some other similar results.

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Acknowledgements

The author is grateful to Shun Watanabe and a reviewer for useful discussions and constructive critical remarks, which improved the paper.

Funding

The research was supported in part by the Russian Foundation for Basic Research, project no. 19-01-00364.

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Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    M. V. Burnashev

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  1. M. V. Burnashev
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Correspondence to M. V. Burnashev.

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Russian Text © The Author(s), 2020, published in Problemy Peredachi Informatsii, 2020, Vol. 56, No. 2, pp. 64–81.

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Burnashev, M.V. New Upper Bounds in the Hypothesis Testing Problem with Information Constraints. Probl Inf Transm 56, 157–172 (2020). https://doi.org/10.1134/S0032946020020027

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  • DOI: https://doi.org/10.1134/S0032946020020027

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