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Optimization Theory, Decision Making, and Operations Research Applications pp 281–291Cite as

Consistent Sequences of Tests Defined by Bans

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 31))

Abstract

Finite probability spaces are important in such problems of operation research as data mining, computer simulation, network and computer security, cryptography and many others. We consider complexity of testing a simple hypothesis H 0,n against complex alternative H 1, n in finite models. The way to make calculation of tests simpler is to build critical sets dependent on smallest bans (the shortest vectors, which have probability zero). We prove necessary and sufficient conditions when consistent sequence of statistical tests exists and all critical sets of the tests are defined by smallest bans. Existence of such sequences of tests is equivalent to existence of strictly consistent sequence of tests.

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Acknowledgements

This work was supported by Russian Foundation for Basic Research, project 10-01-00480.

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Authors and Affiliations

  1. Institute of Informatics Problems, RAS, Vaviliva St., 44, build 2, 119333, Moscow, Russia

    Alexander Grusho

  2. Moscow State University, Leninskie Gory, GSP-2, 119992, Moscow, Russia

    Elena Timonina

Authors
  1. Alexander Grusho
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  2. Elena Timonina
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Corresponding author

Correspondence to Alexander Grusho .

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Editors and Affiliations

  1. , Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece

    Athanasios Migdalas

  2. , Economical and Social Sciences, University of Macedonia, Loggou-Tourpali, Naoussa, 59200, Greece

    Angelo Sifaleras

  3. , Department of Applied Informatics, University of Macedonia, Egnatia St. 156, Thessaloniki, 54006, Greece

    Christos K. Georgiadis

  4. , Department of Marketing and Operations M, University of Macedonia, Agiou Dimitriou 49, Edessa, 58200, Greece

    Jason Papathanasiou

  5. , Department of Applied Informatics, University of Macedonia, Egnatia Street 156, Thessaloniki, 54006, Greece

    Emmanuil Stiakakis

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Grusho, A., Timonina, E. (2013). Consistent Sequences of Tests Defined by Bans. In: Migdalas, A., Sifaleras, A., Georgiadis, C., Papathanasiou, J., Stiakakis, E. (eds) Optimization Theory, Decision Making, and Operations Research Applications. Springer Proceedings in Mathematics & Statistics, vol 31. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5134-1_20

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