On Testing of Hypotheses for Many Independent Objects
Abstract
The problem of many hypotheses testing for a model consisting of three independent objects is considered. It is supposed that M probability distributions are known and each object independently of others follows to one of them. The matrix of asymptotic interdependencies (reliability{reliability functions) of all possible pairs of the error probability exponents (reliabilities) in optimal testing of this model is studied. This problem was introduced (and solved for the case with two given probability distributions) by Ahlswede and Haroutunian. The model with two independent objects with M hypotheses was examined by Haroutunian and Hakobyan.
References
E.A . Haroutunian,"Logarithmically asymptotically optimal testing of multiple statistical hypotheses" , Problems of Control and Information Theory, vol.19(5-6),pp. 413-421,1990.
R.F.Ahlswede and E. A .Haroutunian, " Testing of hypotheses and identification" , Electronic Notes on Discrete Mathematics,vol.21,pp.185-189,005.
E. A .Haroutunian and P.M.Hakobyan,"On logarithmically asymptotically optimal hypothesis testing of three distributions for of independent objects", Mathematical Problems of Computer Science vol.24, pp.76-81,2005.
E. A . Haroutunian and P. M.Hakobyan, " On LA Otesting of multiple hypotheses for pair of objects" , Mathematical Problems of Computer Science vol.25, pp.93-101,2006.
L. Birge, " Vitesses maximals de decroissance des erreurs et tests optimaux associes". Z. Wahrsch. verw. Gebiete,vol. 55, pp.261-273,1981 .
I. Csiszar and J. KÄorner, Information Theory: Coding Theorems for Discrete Memoryless Systems, Academic Press, New York,1981 .
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