Scholarly Research Exchange

Scholarly Research Exchange / 2009 / Article

Research Article | Open Access

Volume 2009 |Article ID 921574 | 6 pages |

Multiple Hypotheses LAO Testing for Many Independent Objects

Received05 Sep 2008
Revised27 May 2009
Accepted15 Jul 2009
Published17 Sep 2009


The procedure of many hypotheses logarithmically asymptotically optimal (LAO) testing for a model consisting of three or more independent objects is analyzed. It is supposed that M probability distributions are known and each object follows one of them independently of others. The matrix of asymptotic interdependencies (reliability-reliability functions) of all possible pairs of the error probability exponents (reliabilities) in optimal testing for this model is studied. This problem was introduced (and solved for the case of two objects and two given probability distributions) by Ahlswede and Haroutunian; it is a generalization of two hypotheses LAO testing problem for one object investigated by Hoeffding, Csiszár and Longo, Tusnády, Longo and Sgarro, Birgé, and others.


  1. R. F. Ahlswede and E. A. Haroutunian, “Testing of hypothesis and identification,” Electronic Notes in Discrete Mathematics, vol. 21, pp. 185–189, 2005. View at: Publisher Site | Google Scholar
  2. R. F. Ahlswede and E. A. Haroutunian, “On logarithmically asymptotically optimal testing of hypotheses and identification,” in General Theory of Information Transfer and Combinatorics, vol. 4123 of Lecture Notes in Computer Science, pp. 462–478, Springer, New York, NY, USA, 2006. View at: Google Scholar
  3. E. A. Haroutunian, “Reliability in multiple hypotheses testing and identification problems,” in Proceedings of the NATO-ASI Conference, vol. 198 of NATO Science Series III: Computer and Systems Sciences, pp. 189–201, IOS Press, Yerevan, Armenia, 2005. View at: Google Scholar
  4. R. E. Bechhofer, J. Kiefer, and M. Sobel, Sequential Identification and Ranking Procedures, The University of Chicago Press, Chicago, Ill, USA, 1968.
  5. R. F. Ahlswede and I. Wegener, Search Problems, John Wiley & Sons, New York, NY, USA, 1987.
  6. W. Hoeffding, “Asymptotically optimal tests for multinomial distributions,” Annals of Mathematical Statistics, vol. 36, pp. 369–401, 1965. View at: Google Scholar
  7. 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. View at: Google Scholar
  8. G. Tusnády, “On asymptotically optimal tests,” Annals of Statistics, vol. 5, no. 2, pp. 385–393, 1977. View at: Google Scholar
  9. G. Longo and A. Sgarro, “The error exponent for the testing of simple statistical hypotheses, a combinatorial approach,” Journal of Combinatories, Informational System Sciences, vol. 5, no. 1, pp. 58–67, 1980. View at: Google Scholar
  10. L. Birgé, “Vitesses maximals de décroissance des erreurs et tests optimaux associeś,” Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 55, pp. 261–273, 1981. View at: Google Scholar
  11. E. A. Haroutunian, “Logarithmically asymptotically optimal testing of multiple statistical hypothyses,” Problems of Control and Information Theory, vol. 19, no. 5-6, pp. 413–421, 1990. View at: Google Scholar
  12. E. A. Haroutunian and P. M. Hakobyan, “On logarithmically asymptotically optimal hypothesis testing of three distributions for pair of independent objects,” Mathematical Problems of Computer Science, vol. 24, pp. 76–81, 2005. View at: Google Scholar

Copyright © 2009 Evgueni Haroutunian and Parandzem Hakobyan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

More related articles

102 Views | 0 Downloads | 0 Citations
 PDF  Download Citation  Citation
 Download other formatsMore
 Order printed copiesOrder

Related articles

We are committed to sharing findings related to COVID-19 as quickly and safely as possible. Any author submitting a COVID-19 paper should notify us at to ensure their research is fast-tracked and made available on a preprint server as soon as possible. We will be providing unlimited waivers of publication charges for accepted articles related to COVID-19. Sign up here as a reviewer to help fast-track new submissions.