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Probabilistic Methods and Distributed Information pp 509–532Cite as

Hypothesis Testing Under Communication Constraints

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Part of the book series: Foundations in Signal Processing, Communications and Networking ((SIGNAL,volume 15))

Abstract

A new class of statistical problems is introduced, involving the presence of communication constraints on remotely collected data. Bivariate hypothesis testing, \(H_0: P_{XY}\) against \(H_1: P_{\bar{XY}}\), is considered when the statistician has direct access to Y data but can be informed about X data only at a prescribed finite rate R. For any fixed R the smallest achievable probability of an error of type 2 with the probability of an error of type 1 being at most \(\epsilon \) is shown to go to zero with an exponential rate not depending on \(\epsilon \) as the sample size goes to infinity.

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Author information

Authors and Affiliations

  1. Bielefeld, Germany

    Rudolf Ahlswede

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  1. Rudolf Ahlswede
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Correspondence to Rudolf Ahlswede .

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Editors and Affiliations

  1. Bielefeld, Germany

    Alexander Ahlswede

  2. Faculty of Mathematics and Computer Sciences, Friedrich-Schiller-University Jena, Jena, Germany

    Ingo Althöfer

  3. Institute for Communications Engineering, Technical University of Munich, München, Bayern, Germany

    Christian Deppe

  4. Applied Mathematics and Statistics, Quantitative Methods, Bielefeld University of Applied Sciences, Bielefeld, Germany

    Ulrich Tamm

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Ahlswede, R. (2019). Hypothesis Testing Under Communication Constraints. In: Ahlswede, A., Althöfer, I., Deppe, C., Tamm, U. (eds) Probabilistic Methods and Distributed Information. Foundations in Signal Processing, Communications and Networking, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-030-00312-8_22

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  • DOI: https://doi.org/10.1007/978-3-030-00312-8_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00310-4

  • Online ISBN: 978-3-030-00312-8

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