On LAO Two-stage Testing of Multiple Hypotheses Concerning Markov Chain

Authors

  • Evgueni A. Haroutunian Institute for Informatics and Automation Problems of NAS RA
  • Parandzem M. Hakobyan Institute for Informatics and Automation Problems of NAS RA
  • Aram O. Yesayan Institute for Informatics and Automation Problems of NAS RA

Keywords:

Logarithmically asymptotically optimal (LAO) test, Reliabilities matrix, Error probability exponent, Markov chain

Abstract

Two-stage testing of multiple hypotheses concerning Markov chain with two separate families of hypothetical transition probabilities is considered. The matrix of reliabilities of logarithmically asymptotically optimal hypotheses testing by a pair of stages is studied and compared with the case of similar one-stage testing. It is shown that two-stage testing needs less operations than one-stage testing.

References

E. Haroutunian, P. Hakobyan and F. Hormozinejad, “On Two-stage LAO testing of multiple hypotheses for the families of distributions", International Journal of Ststistics and Econometrics Methods, vol. 2, no. 2, pp. 127-156, 2013.

E. L. Lehmann and J. P. Romano, Testing Statistical Hypotheses, Third Edition. Springer, New York, 2005.

W. Hoeffding, “A symptotically optimal tests for multinomial distributions", 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 Scientiarum Mathematicarum 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. Tusnády, “Testing statistical hypotheses (an information theoretic approach)", Preprint of the Mathematical Institute of the Hungarian Academy of Sciences, Budapest (Part 1, 1979, Part 2, 1982).

G. Longo and A. Sgarro, “The error exponent for the testing of simple statistical hypotheses: A combinatorial approach", Journal of Combinatorics, Information and System Sciences, 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.

M. Feder and N. Merhav, “Universal composit hypothesis testing: a competititve minimax approach", IEEE Transactions on Information Theory, vol. 48, no. 6, pp. 1504-1517, 2002.

E. Levitan and N. Merhav, “A competitive Neyman-Pearson approach to universal hypothesis testing with applications", IEEE Transactions on Information Theory, vol. 48, no. 8, pp. 2215-2229, 2002.

S. Natarajan, “Large deviations, hypotheses testing, and source coding for finite Markov chains," IEEE Transactions on Information Theory, vol. 31, no. 3, pp. 360-365, 1985.

E. A. Haroutunian, “Logarithmically asymptotically optimal testing of multiple statistical hypotheses," Problems of Control and Information Theory, vol. 19, no. 5-6, pp. 413-421, 1990.

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.

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. H aroutunian, “On asymptotically optimal criteria for Markov chains", (in Russian), First World Congress of Bernoulli Society, vol. 2, no. 3, pp. 153-156, 1989.

E. A. Haroutunian, “Asymptotically optimal testing of many statistical hypotheses concerning Markov Chain" (in Russian), 5-th International Vilnius Conferance on Probability Theory and Mathem. Statistics, vol. 1, (A-L), pp. 202-203, 1989.

E. Haroutunian, “Reliability in multiple hypotheses testing and identification problem", in Data Fusion for Situation Monitoring, Incident Detection, Alert and Respons Management, NATO Science Series: Computer and System Sciences, IOS Press, vol. 198, pp. 189-201, 2005.

E. Haroutunian and P. Hakobyan, “On multiple hypotheses testing for many independent objects", VII International School-seminar “Multidementional statistical analysis and econometrics", pp. 78,79, Tsakhadzor, 2008.

E. Haroutunian and N. Grigoryan, “On reliability approach for testing of many distributions for pair of Markov chains", Transactions of IIAP NAS RA, Mathematical Problems of Computer Science, vol. 29, pp. 99-96, 2007.

E. Haroutunian and N. Grigoryan, “On arbitrarily varying Markov source coding and hypothesis LAO testing by non-informed statistician", Proc. of IEEE Internatioan Symposium Information Theory, Seoul, South Korea, pp. 981-985, 2009.

R. F. Ahlswede and E. A. Haroutunian, “On logarithmically asymptotically optimal testing of hypotheses and identification", Lecture Notes in Computer Science, vol. 4123,

E. A. Haroutunian and P. M. Hakobyan, “Remarks about reliable identification of probability distributions of two independent objects", Transactions of IIAP of NAS of RA, Mathematical Problems of Computer Science. vol. 33, pp. 91-94, 2010

E. A. Haroutunian, A. O. Yessayan and P. M. Hakobyan, “On reliability approach to multiple hypotheses testing and identification of probability distributions of two stochastically coupled objects", International Journal “Informations Theories and Applications", vol. 17, no. 3, pp. 259-288, 2010.

E. A. Haroutunian and A. O. Yessayan, “On reliability approach to multiple hypotheses testing and to identification of probability distributions of two stochastically related objects", Proc. of IEEE Internation Sympos. Information Theory, Seint-Peterburg, Russia, pp. 2671-2675, 2011.

E. A. Haroutunian and L. Navaei, “On optimal identification of Markov chain distributions subject to the reliability criterion", Transactions of IIAP NAS RA, Mathematical Problems of Computer Science, vol. 32, pp.66-70, 2009.

L. Navaei, “On reliable identification of two independent Markov chain distributions", Transactions of IIAP NAS RA, Mathematical Problems of Computer Science, vol. 32, pp.74-77, 2009.

R. F. Ahlswede and E. A. Haroutunian, “General Theory of Information Transfer and Combinatorics", Springer Verlag, pp. 462- 478, 2006.

Downloads

Published

2021-12-10

How to Cite

Haroutunian, E. A. ., Hakobyan, P. M. ., & Yesayan, A. O. . (2021). On LAO Two-stage Testing of Multiple Hypotheses Concerning Markov Chain. Mathematical Problems of Computer Science, 41, 63–73. Retrieved from http://mpcs.sci.am/index.php/mpcs/article/view/231

Most read articles by the same author(s)

<< < 1 2