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New methods for statistical decision making in conditions of a limited volume of observations and with a prioriy parametric uncertainty
- Authors: Mkrtchyan F.A.1
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Affiliations:
- Fryazino Branch Kotelnikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences
- Issue: Vol 69, No 1 (2024)
- Pages: 76-87
- Section: ТЕОРИЯ И МЕТОДЫ ОБРАБОТКИ СИГНАЛОВ
- URL: https://kazanmedjournal.ru/0033-8494/article/view/650721
- DOI: https://doi.org/10.31857/S0033849424010064
- EDN: https://elibrary.ru/KZVMIA
- ID: 650721
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Abstract
A new generalized adaptive algorithm for learning to make statistical decisions for exponential families of distributions with a priori parametric uncertainty in conditions of small samples has been developed. A generalized decision rule is presented, obtained by estimating unknown parameters of distributions, as well as a decision rule that satisfies the necessary optimality conditions: constancy of the average probability of a type I error and unbiasedness. Specific decision procedures for partial distributions obtained from a generalized algorithm are considered. Numerical examples are given. The effectiveness of the developed optimal procedure for small samples is shown.
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About the authors
F. A. Mkrtchyan
Fryazino Branch Kotelnikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences
Author for correspondence.
Email: ferd47@mail.ru
Russian Federation, Fryazino, Moscow region, 141190 Russia
References
- Арманд Н.А., Крапивин В.Ф., Мкртчян Ф.А. Методы обработки данных радиофизического исследования окружающей среды. М.: Наука, 1987.
- Мкртчян Ф.А. Оптимальное различение сигналов и проблемы мониторинга. М.: Наука, 1982.
- Mkrtchyan F.A., Varotsos C.A. // Water, Air, & Soil Pollution. 2018. V. 229. № 8. Article No. 273.
- Данков П.П. // РЭ. 1965. Т. 10. № 10. С. 1774.
- Леман Э. Проверка статистических гипотез. М.: Наука, 1979.
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