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The paper considers the problem of joint estimation of object parameters and
statistical characteristics of random disturbances based on data from independent experiments. It is
indicated that the use of the method of moments for the problem under consideration gives estimates
that are not effective in the Rao-Kramer sense and the most common asymptotically effective estimation
method, in this sense, is the maximum likelihood method(ML). However, in the case of objects with
several disturbances that have distribution densities of a general form, the implementation of the ML
method is difficult, since to find the values of the distribution density it is necessary to calculate (q 1)
-dimensional integrals. The presented minimum distance (MD) method can be applied to find joint
estimates of the object parameters and the parameters of random disturbances. MD estimates with
weight matrices independent of the parameters can be taken as consistent parameter estimates. It is
noted that, in contrast to the method of moments, the MD method allows solving the identification
problem in the case of disturbances with unlimited dispersions.
 

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  • DOI
  • UzSCI тизимида яратилган сана 11-02-2025
  • Ўқишлар сони 22
  • Нашр санаси 07-02-2025
  • Мақола тилиIngliz
  • Саҳифалар сони46-49
English

The paper considers the problem of joint estimation of object parameters and
statistical characteristics of random disturbances based on data from independent experiments. It is
indicated that the use of the method of moments for the problem under consideration gives estimates
that are not effective in the Rao-Kramer sense and the most common asymptotically effective estimation
method, in this sense, is the maximum likelihood method(ML). However, in the case of objects with
several disturbances that have distribution densities of a general form, the implementation of the ML
method is difficult, since to find the values of the distribution density it is necessary to calculate (q 1)
-dimensional integrals. The presented minimum distance (MD) method can be applied to find joint
estimates of the object parameters and the parameters of random disturbances. MD estimates with
weight matrices independent of the parameters can be taken as consistent parameter estimates. It is
noted that, in contrast to the method of moments, the MD method allows solving the identification
problem in the case of disturbances with unlimited dispersions.
 

№ Муаллифнинг исми Лавозими Ташкилот номи
1 Mukhtarkhodjaevna Y.A. PhD, Associate Professor Tashkent State Technical University
№ Ҳавола номи
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3 11. Mikhailov, R. G. Application of statistical methods in engineering problems. - Chelyabinsk: Publishing house of ChSTU, 2020. - 275 p. 12. Smith, A., & Taylor, B. (2022). "Integrating Statistical Analysis in the Assessment of Disturbing Influences on Dynamic Systems." In Proceedings of the World Congress on Engineering, 789-794. 13. Serebryannaya L.V., Tretyakov F.I. Methods and algorithms for decision making: educational method. allowance. Minsk; BSUIR.2016 – 64. : ill. 14. Koleshko V.M., Samoshkin M.A. Algorithms for recognition and identification of patterns and images. Artificial Intelligence No. 3 p.476-483, 2004. 15. Baronkin V.M., Gladilin A.V. Estimation of parameters of the covariance matrix of structural noise // Proceedings of the Central Research Institute named after. acad. A. N. Krylova. No. 41, 2008. - pp. 198-204.
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