On Two-stage Logarithmically Asymptotically Optimal Testing of Multiple Hypotheses Concerning Distributions from the Pair of Families

Authors

  • Evgueni Haroutunian Institute for Informatics and Automation Problems of NAS RA
  • Parandzem Hakobyan Institute for Informatics and Automation Problems of NAS RA
  • Farshin Hormozi nejad Islamic Azad University, Ahvaz Branch, Iran

Keywords:

Logarithmically asymptotically optimal (LAO) test, reliabilities matrix, error probability exponent

Abstract

Two-stage testing of multiple hypotheses for a model with two given families of hypothetical probability distributions 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.

References

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

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

I. Csiszár and J. Körner. Information Theory: Coding Theorems for Discrete Memoryless Systems, Academic press, New York, 1981.

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.

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.A. Haroutunian. “Reliability in multiple hypotheses testing and identification", Proceedings of the NATO-ASI Conference, vol. 198 of NATO Science Series III: Computer and Systems Sciences, Yerevan, Armenia, pp. 189-201, IOS Press, 2008.

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

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

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

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Published

2021-12-10

How to Cite

Haroutunian, E. ., Hakobyan, P. ., & Hormozi nejad, F. . (2021). On Two-stage Logarithmically Asymptotically Optimal Testing of Multiple Hypotheses Concerning Distributions from the Pair of Families. Mathematical Problems of Computer Science, 37, 25–34. Retrieved from http://mpcs.sci.am/index.php/mpcs/article/view/247

Issue

Vol. 37 (2012): Mathematical Problems of Computer Science

Section

Articles

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