Multiple Hypotheses LAO Testing for Many Independent Objects
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 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.
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
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
R. E. Bechhofer, J. Kiefer, and M. Sobel, Sequential Identification and Ranking Procedures, The University of Chicago Press, Chicago, Ill, USA, 1968.
R. F. Ahlswede and I. Wegener, Search Problems, John Wiley & Sons, New York, NY, USA, 1987.
W. Hoeffding, “Asymptotically optimal tests for multinomial distributions,” Annals of Mathematical Statistics, vol. 36, pp. 369–401, 1965.View at: Google Scholar
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
G. Tusnády, “On asymptotically optimal tests,” Annals of Statistics, vol. 5, no. 2, pp. 385–393, 1977.View at: Google Scholar
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
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
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
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