Ukrainian Mathematical Journal

, Volume 71, Issue 4, pp 554–571 | Cite as

Consistent Criteria for Hypotheses Testing

  • Z. S. Zerakidze
  • O. G. PurtukhiaEmail author

We investigate statistical structures that admit consistent criteria for hypotheses testing and establish necessary and sufficient conditions for the existence of consistent criteria for hypotheses testing.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    I. Sh. Ibramkhalilov and A. V. Skorokhod, Consistent Estimates for the Parameters of Random Process [in Russian], Naukova Dumka, Kiev (1980).zbMATHGoogle Scholar
  2. 2.
    T. Jech, Set Theory, Springer, Berlin, (2003).zbMATHGoogle Scholar
  3. 3.
    A. B. Kharazishvili, Topological Aspects of the Measure Theory [in Russian], Naukova Dumka, Kiev (1984).Google Scholar
  4. 4.
    Z. S. Zerakidze, “On weakly separable and separable families of probability measures,” Soobshch. Akad. Nauk Gruz. SSR, 113, No. 2, 273–275 (1984).MathSciNetzbMATHGoogle Scholar
  5. 5.
    Z. S. Zerakidze, “Hilbert space of measures,” Ukr. Mat. Zh., 38, No. 2, 147–153 (1986); English translation:Ukr. Math. J., 38, No. 2, 131–135 (1986).Google Scholar
  6. 6.
    Z. Zerakidze and M. Mumladze, Statistical Structures and Consistent Criteria for Checking Hypotheses, Lambert Academic Publishing, Saarbrucken, Deutschland (2015).zbMATHGoogle Scholar
  7. 7.
    G. Pantsulaia, “On orthogonal families of probability measures,” Trans. GP., 1, No. 8, 106–112 (1989).Google Scholar
  8. 8.
    G. Pantsulaia, “On separation properties for families of probability measures,” Georg. Math. J., 10, No. 2, 335–341 (2003).MathSciNetzbMATHGoogle Scholar
  9. 9.
    Z. Zerakidze and O. Purtukhia, “The weakly consistent, strongly consistent, and consistent estimates of the parameters,” in: Rep. Enlarged Sess. Semin. Vekua Inst. Appl. Math., 31 (2017), pp. 151–154.Google Scholar
  10. 10.
    S. N. Krasnitskii, “On the conditions of equivalence and orthogonality of measures corresponding to homogeneous Gaussian fields,” Teor. Ver. Ee Primen., 18, No. 3, 615–621 (1973).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Gori State UniversityGoriGeorgia
  2. 2.Dzhavakhishvili Tbilisi State UniversityTbilisiGeorgia

Personalised recommendations