Subordinate statistical structures
Authors:
Z. K. Zerakidze and G. A. Sokhadze
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 85 (2012), 73-81
MSC (2010):
Primary 62H05, 62H12
DOI:
https://doi.org/10.1090/S0094-9000-2013-00875-8
Published electronically:
January 11, 2013
MathSciNet review:
2933704
Full-text PDF Free Access
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Additional Information
Abstract: General statistical structures are considered in this paper. It is shown that a general statistical structure can be reduced to some orthogonal or absolutely continuous statistical structure.
References
- I. Š. Ibramhalilov and A. V. Skorohod, Sostoyatel′nye otsenki parametrov sluchaĭ nykh protsessov, “Naukova Dumka”, Kiev, 1980 (Russian). MR 584624
- Z. S. Zerakidze, A Hilbert space of measures, Ukrain. Mat. Zh. 38 (1986), no. 2, 148–154, 267 (Russian). MR 841043
- F. R. Drake, Set Theory: An Introduction to Large Cardinals, North-Holland Publishing Company, Amsterdam, 1974.
- Z. S. Zerakidze, Weakly separable and separable families of probability measures, Soobshch. Akad. Nauk Gruzin. SSR 113 (1984), no. 2, 273–275 (Russian, with English and Georgian summaries). MR 780715
References
- I. M. Ibramkhalilov and A. V. Skorokhod, Consistent Estimators of Parameters of Random Processes, “Naukova Dumka”, Kiev, 1980. (Russian) MR 584624 (82h:62140)
- Z. S. Zerakidze, A Hilbert space of measures, Ukr. Math. J. 38 (1986), no. 2, 148–154. MR 841043 (88f:46062)
- F. R. Drake, Set Theory: An Introduction to Large Cardinals, North-Holland Publishing Company, Amsterdam, 1974.
- Z. S. Zerakidze, Weakly separable and separable families of probability measures, Soobshch. Akad. Nauk Gruzin. SSR 113 (1984), no. 2, 273–275. (Russian) MR 780715 (86e:28010)
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Additional Information
Z. K. Zerakidze
Affiliation:
Gori State University, Chavchavadze Street, 53, Gori, Georgia
Email:
z.zerakidze@gmail.ru
G. A. Sokhadze
Affiliation:
Ilia Vekua Institute of Applied Mathematics, University Street 3, Tbilisi, 0186, Georgia
Email:
giasokhi1@i.ua
Keywords:
Statistical structures,
absolute continuity,
orthogonality
Received by editor(s):
July 27, 2011
Published electronically:
January 11, 2013
Additional Notes:
The paper is based on the talk presented at the International Conference “Modern Stochastics: Theory and Applications II” held September 7–11, 2010, at Kyiv National Taras Shevchenko University and dedicated to the anniversaries of prominent Ukrainian scientists, Anatoliĭ Skorokhod, Vladimir Korolyuk, and Igor Kovalenko
Article copyright:
© Copyright 2013
American Mathematical Society
