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The consistent criteria of hypotheses
Volume 1, Issue 1 (2014), pp. 3–11
L. Aleksidze   M. Mumladze   Z. Zerakidze  

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https://doi.org/10.15559/vmsta-2014.1.1.5
Pub. online: 27 June 2014      Type: Research Article      Open accessOpen Access

Received
30 January 2013
Revised
4 March 2014
Accepted
5 June 2014
Published
27 June 2014

Abstract

In this paper we define the consistent criteria of hypotheses such as the probability of any kind of errors is zero for given criteria. We prove necessary and sufficient conditions for the existence of such criteria.

References

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Borovkov, A.A.: Mathematical Statistics. Nauka, Moscow (1984). English translation, Gordon and Breach, Amsterdam (1998)
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Ibramkhalilov, Sh. Skorokhod A. V, I.: Consistent Estimates of Parameters of Random Processes. Naukova Dumka, Kiev (1980)
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Jech, T.: Set Theory. Springer, Berlin (2003). MR1940513
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Kharazishvili, A.B.: Topological Aspects of Measure Theory. Naukova Dumka, Kiev (1984). MR0784614
[5] 
Maleev, M., Serechenko, A., Tarashchanskii, M.: Family of probability measures admitting consistent estimators. In: Skorokhod, A.V. (ed.) Probability Distributions in Infinite Dimensional Spaces, pp. 125–134. Institute of Mathematics of Acad. Sci. Ukrainian SSR, Kiev (1978)
[6] 
Zerakidze, Z.: On weakly divisible and divisible families of probability measures. Bull. Acad. Sci. Georgian SSR 113(2), 273–275 (1984). MR0780715
[7] 
Zerakidze, Z.: On consistent estimators for families of probability measures. In: 5-th Japan–USSR Symposium on Probability Theory, Kyoto, pp. 62–63 (1986)
[8] 
Zerakidze, Z.S.: Banach space of measures. In: Grigelionis, B., et al. (eds.) Probability Theory and Mathematical Statistics: Proceedings of the Fifth Vilnius Conference, Vilnius, vol. 2, VSP/Mokslas, pp. 609–616 (1991). MR1153917

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© 2014 The Author(s). Published by VTeX
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Keywords
Consistent criteria singular orthogonal weakly separable strongly separable probability measures

MSC2010
62H05 62H12

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