On Logarithmically Asymptotically Optimal Testing of Hypotheses and Identification

  • R. Ahlswede
  • E. Haroutunian
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4123)


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.


Hypothesis Testing Error Probability Ranking Problem IEEE Trans Inform Theory Independent Object 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • R. Ahlswede
    • 1
  • E. Haroutunian
    • 2
  1. 1.Fakultät für MathematikUniversität BielefeldBielefeldGermany
  2. 2. 

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