Achievable region of reliabilities in multiple hypotheses two-stage testing for the pair of families of distributions

  • Authors

    • Farshin Hormozi-Nejad Department of Mathematics and Statistics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran
    2014-09-20
    https://doi.org/10.14419/ijamr.v3i4.3060
  • The achievable region of reliabilities in the model with several possible hypothetical probability distributions partitioned into the pair of families is considered. The achievable region for many hypotheses testing was examined by Tuncel. Decisions concerning realized probability distribution of the object must be made on the base of the samples which are received in each stage of the two-stage test. It is proved that the defined region for the vectors of reliabilities in the two-stage test characterizes the set of all achievable vectors and advantages of the two-stage testing are revealed.

    Keywords: LAO test, method of types, multiple hypotheses testing, reliability, two-stage test.

  • References

    1. R. Ahlswede and E.A. Haroutunian, On statistical hypotheses optimal testing and identification, Lecture Notes in Computer Science, General Theory of Information Transfer and Combinatorics, Springer, 4123 (2006),462-478.
    2. T.M. Cover and J.A. Tomas, Element of information theory, (Second Edition), Wiley, New York, 2006.
    3. I. Csisz´ar and J. K¨orner, Information theory: coding theorems for discrete memoryless systems, Academic Press, New York, 1981.
    4. I. Csisz´ar and P.C. Shields, Information theory and statistics: a tutorial, Foundations and Trends in Communications and Information Theory, 1:4 (2004), 417-528.
    5. S. Dudua and M.J. Van Der Laon, Multiple testing procedures with application to genomics, Springer, 2008.
    6. E.A. Haroutunian, Logarithmically asymptotically optimal testing of multiple statistical hypotheses, Problems of Control and Information Theory, 19 (1990), 413-421.
    7. E.A. Haroutunian, M.E. Haroutunian and A.N. Haroutunyan, Reliability criteria in information theory and in statistical hypothesis testing, Foundations and Trends in Communications and Information Theory, 4:2-3 (2008), 97-263.
    8. E.A. Haroutunian, P.M. Hakobyan and F. Hormozi-nejad, On two-stage LAO testing of multiple hypotheses for a pair of families of probability distributions, Journal of Statistical and Econometric Methods, 2:2 (2013), 127-156.
    9. W. Hoefding, Asymptotically optimal tests for multinomial distributions, Annals of Mathematical Statistics, 36 (1965), 369-401.
    10. E.L. Lehman and J.P. Romano, Testing statistical hypotheses, (2nd Edition), Springer, 2005.
    11. E. Tuncel, On error exponents in hypothesis testing, IEEE Trans. Inf. Theory, 51:8 (2005), 2945-2950.
    12. G. Tusnady, On asymptotically optimal tests, Annals of Statistics, 5:2 (1977), 385-393.
    13. A.O. Yessayan, E.A. Haroutunian and P.M. Hakobyan, Error probability exponents and achievable region in testing of many hypotheses for two independent objects, Mathematical Problems of Computers Science, 35 (2011), 33-36.
  • Downloads

  • How to Cite

    Hormozi-Nejad, F. (2014). Achievable region of reliabilities in multiple hypotheses two-stage testing for the pair of families of distributions. International Journal of Applied Mathematical Research, 3(4), 407-415. https://doi.org/10.14419/ijamr.v3i4.3060