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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This work was supported by Russian Foundation for Basic Research, project 10-01-00480.
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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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DOI: https://doi.org/10.1007/978-1-4614-5134-1_20
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