New methods for statistical decision making in conditions of a limited volume of observations and with a prioriy parametric uncertainty

Mkrtchyan, F. A.

doi:10.31857/S0033849424010064

PII

10.31857/S0033849424010064-1

DOI

10.31857/S0033849424010064

Publication type

Article

Status

Published

Authors

F. A. Mkrtchyan

Affiliation: Fryazino Branch Kotelnikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences

Volume/ Edition

Volume 69 / Issue number 1

Pages

76-87

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.

Keywords

априорная параметрическая неопределённость обобщенный адаптивный алгоритм экспоненциальное семейство распределений выборки малого объема

Date of publication

16.09.2025

Year of publication

2025

Number of purchasers

Views

References

1. Арманд Н.А., Крапивин В.Ф., Мкртчян Ф.А. Методы обработки данных радиофизического исследования окружающей среды. М.: Наука, 1987.
2. Мкртчян Ф.А. Оптимальное различение сигналов и проблемы мониторинга. М.: Наука, 1982.
3. Mkrtchyan F.A., Varotsos C.A. // Water, Air, & Soil Pollution. 2018. V. 229. № 8. Article No. 273.
4. Данков П.П. // РЭ. 1965. Т. 10. № 10. С. 1774.
5. Леман Э. Проверка статистических гипотез. М.: Наука, 1979.

GOST	Mkrtchyan F. New methods for statistical decision making in conditions of a limited volume of observations and with a prioriy parametric uncertainty // Journal of Communications Technology and Electronics. – 2024. – V. 69. – Issue number 1 C. 76-87 . URL: https://radiotechras.ru/10-31857-s0033849424010064-1/?version_id=111025. DOI: 10.31857/S0033849424010064
MLA	Mkrtchyan, F. A "New methods for statistical decision making in conditions of a limited volume of observations and with a prioriy parametric uncertainty." Journal of Communications Technology and Electronics. 69.1 (2024).:76-87. DOI: 10.31857/S0033849424010064
APA	Mkrtchyan F. (2024). New methods for statistical decision making in conditions of a limited volume of observations and with a prioriy parametric uncertainty. Journal of Communications Technology and Electronics. vol. 69, no. 1, pp.76-87 DOI: 10.31857/S0033849424010064

RAS PhysicsРадиотехника и электроника Journal of Communications Technology and Electronics

New methods for statistical decision making in conditions of a limited volume of observations and with a prioriy parametric uncertainty

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RAS PhysicsРадиотехника и электроника Journal of Communications Technology and Electronics

New methods for statistical decision making in conditions of a limited volume of observations and with a prioriy parametric uncertainty

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