# Many Hypotheses LAO Testing With Rejection of Decision for Arbitrarily Varying Object

## Abstract

The model of multiple statistical hypotheses testing with possibility rejecting to make choices between hypotheses concerning discrete arbitrarily varying object is investigated. The optimal procedure of decisions is shown. The matrix of optimal asymptotical interdependencies (reliability-reliability functions) of all possible pairs of the error probability exponents (reliabilities) is studied for arbitrarily varying object with the current states sequence known to the statistician.

## References

W. Hoeffding, “Asymptotically optimal tests for multinomial distributions, "The Annals of Mathematical Statistics, vol. 36, pp. 369-401, 1965.

I.Csiszár and G. Longo, “On the error exponent for source coding and for testing simple statistical hypotheses", Studia Sc. Math. Hungarica, vol. 6, pp. 181-191, 1971.

G. Tusnády, “On asymptotically optimal tests," Annals of Statatistics, vol. 5, no. 2, pp. 385-393, 1977.

G. Longo and A. Sgarro, “The error exponent for the testing of simple statistical hypotheses: A combinatorial approach", Journal of Combinatorics and Informational System Science, vol. 5, no. 1, pp. 58-67, 1980.

L. Birgé, “Vitesses maximals de déroissence des erreurs et tests optimaux associés". Z. Wahrsch. verw. Gebiete, vol. 55, pp. 261-273, 1981.

S. Natarajan, “Large derivations hypothesis testing and source coding for finite Markov chains", IEEE Trans. Inform. Theory, vol. 31, no. 3, pp. 360-365, 1985.

M. Gutman, “Asymptotically optimal classification for multiple tests with empirically observed statistics", IEEE Transactions on Information Theory, vol. 35, no. 2, pp. 401-408, 1989.

V. Anantharam, “A large deriations approach to error exponent in source coding and hypotheses testing", IEEE Trans. Inform. Theory, vol. 36, no. 4, pp. 938-943, 1990.

T.S. Han, “Hypothesis testing with the general source", IEEE Transactions on Information Theory, vol. 46, no. 7, pp. 2415-2427, 2000.

E.A. Haroutunian, “Many statistical hypotheses: interdependence of optimal test's error probabilities exponents", (In Russian), Abstract of the report on the 3rd All-Union school-seminar, "Program-algorithmical software for applied multi-variate statistical analysis", Tsakhkadzor, Part 2, pp. 177-178, 1988.

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.

E. Haroutunian and P. Hakobyan, “On multiple hypotheses testing by informed statistician for arbitrarily varying object and application to source coding", Transactions of IIAP of NAS of RA and of YSU, Mathematical Problems of Computer Science, vol. 23, pp. 36-46, 2004.

F.W. Fu and S.Y. Shen, “Hypothesis testing for arbitrarily varying source with exponential-type constraint, "IEEE Transactions on Information Theory, vol. 44, no. 2, pp. 892-895, 1998.

R.F. Ahlswede, E. Aloyan and E. Haroutunian, “On logarithmically asymptotically optimal hypothesis testing for arbitrarily varying source with side information, "Lecture Notes in Computer Science, Volume 4123," General Theory of Information Transfer and Combinatorics", Springer, pp. 457-461, 2006.

M.S. Nikulin, “On one result of L.N. Bolshev from theory of hypotheses statistical testing", (In Russian), Studies on Mathematical Statistics. Notes of Scientific Seminars of Saint-Petersburg Branch of the Mathematical Institute, vol. 7, pp. 129-137, 1986.

I.Csiszár and J. Körner, “Information theory: coding theorems for discrete memoryless systems", Academic press., New York, 1981.

R.E. Blahut, “Hypothesis testing and information theory, "IEEE Transactions on Information Theory, vol. 20, no. 4, pp. 405-417, 1974.

T.M. Cover and J.A. Thomas, Elements of Information Theory. Second Edition, New York, Wiley, 2006.

I. Csiszár and P. Shields, “Information theory and statistics: A tutorial", Foundations and Trends in Communications and Information Theory, 2004.

R.F. Ahlswede and E.A. Haroutunian, “On logarithmically asymptotically optimal testing of hypotheses and identification", Lecture Notes in Computer Science, volume 4123," General Theory of Information Transfer and Combinatorics", Springer, pp. 462-478, 2006.

E. Haroutunian, M. Haroutunian and A. Harutyunyan, “Reliability criteria in information theory and in statistical hypothesis testing", Foundations and Trends in Communications and Information Theory, vol. 4, no. 2-3, 2008, 171 P.

E. Haroutunian and P. Hakobyan, “Multiple hypotheses LAO testing for many independent objects", International Journal “Scholarly Research Exchange", pp. 1-6, 2009.

## Downloads

## Published

## How to Cite

*Mathematical Problems of Computer Science*,

*35*, 77–85. Retrieved from http://mpcs.sci.am/index.php/mpcs/article/view/289

## Issue

## Section

## License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.