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On Logarithmically Asymptotically Optimal Testing of Hypotheses and Identification

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General Theory of Information Transfer and Combinatorics

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4123))

Abstract

We introduce a new aspect of the influence of the information-theoretical methods on the statistical theory. The procedures of the probability distributions identification for K(≥1) random objects each having one from the known set of M(≥2) distributions are studied. N-sequences of discrete independent random variables represent results of N observations for each of K objects. On the base of such samples decisions must be made concerning probability distributions of the objects. For \(N \longrightarrow \infty\) the exponential decrease of the test’s error probabilities is considered. The reliability matrices of logarithmically asymptotically optimal procedures are investigated for some models and formulations of the identification problems. The optimal subsets of reliabilities which values may be given beforehand and conditions guaranteeing positiveness of all the reliabilities are investigated.

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Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, Universitätsstr. 25, 33615, Bielefeld, Germany

    R. Ahlswede

  2.  

    E. Haroutunian

Authors
  1. R. Ahlswede
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  2. E. Haroutunian
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Editor information

Editors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, 100131, 33501, Bielefeld, Germany

    Rudolf Ahlswede

  2. Fakultät für Mathematik, Universität Bielefeld, Universitätsstr. 25, 33615, Bielefeld, Germany

    Lars Bäumer , Ning Cai , Harout Aydinian  & Christian Deppe , ,  & 

  3. Russian Academy of Sciences Institute of Problems of Information Transmission, Bol’shoi Karetnyi per. 19, 101447, Moscow, Russia

    Vladimir Blinovsky

  4. Universität Bielefeld, Fakultät für Mathematik, Universitätsstr. 25, 33615, Bielefeld, Germany

    Haik Mashurian

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Ahlswede, R., Haroutunian, E. (2006). On Logarithmically Asymptotically Optimal Testing of Hypotheses and Identification. In: Ahlswede, R., et al. General Theory of Information Transfer and Combinatorics. Lecture Notes in Computer Science, vol 4123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889342_33

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  • DOI: https://doi.org/10.1007/11889342_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46244-6

  • Online ISBN: 978-3-540-46245-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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