Error Probability Exponents and Achievable Region in Testing of Many Hypotheses for Two Independent Objects
Abstract
The model of many hypotheses testing for one objects was examined by E. Tuncel. In the present work it is supposed that L hypothetical probability distributions are known and two objects independently each from other follow to one of them. N-vectors of values of discrete independent random variables represent results of N observations for each object. Decisions concerning realized probability distributions of the objects must be made on the base of such samples. It is proved that defined region for vector of error probability exponents “reliabilities for two objects completely characterizes set of all achievable vectors.
References
I. Csiszár and P.C. Shields, Information Theory and Statistics: a tutorial. Foundations and Trends in Communications and Information Theory, volume 1, no. 4, 2004.
T.M. Cover and J.A. Thomas, Elements of Information Theory, Second Edition, Wiley, New York, 2006.
R.E. Bechhofer, J. Kiefer and M. Sobel, Sequential Identification and Ranking Procedures. The University of Chicago, Press, 1968.
R.E. Blahut, “Hypotheses testing and information theory, "IEEE Transaction on Information Theory, vol 20, pp. 405-417, 1974.
R.E. Blahut, Principles and Practice of Information Theory. Reading, MA: Addison-Wesley, 1987.
E. Tuncel, “On error exponents in hypothesis testing", IEEE Trans. Inf. Theory, vol. 51, no. 8, pp. 2945-2950, 2005.
E. 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, “On logarithmically asymptotically optimal testing of hypotheses and identification". Lecture Notes in Computer Science, vol. 4123, “General Theory of Information Transfer and Combinatorics", Springer, pp. 462-478, 2006.
E. Haroutunian, “Reliability in multiple hypotheses testing and identification", Proceedings of NATO ASI, Yerevan, 2003, NATO Science Series III: Computer and System Sciences, vol. 198, pp. 189-201, IOS Press, 2005.
E. Haroutunian and P. Hakobyan, “Multiple hypotheses LAO testing for many independent objects", International Journal Scholarly Research Exchange, vol. 2009, pp. 1-6, 2009.
E. Haroutunian and A. Yessayan, “On optimal testing of three hypotheses for two dependent objects", Mathematical Problems of Computer Sciences, vol. XXVI, pp. 89-94, 2006.
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