The analysis of polynomial method on evaluation of parameter of correlated non-gaussian random quantity

Authors

DOI:

https://doi.org/10.15587/1729-4061.2014.20023

Keywords:

evaluation of parameters, sample, non-Gaussian random quantity, correlation, polynomial maximization method

Abstract

One of the possible solutions of the evaluation problem of parameters of non-Gaussian random quantities at their moment-cumulant description at the correlated sample is considered in the paper. The analysis of the algorithm of the adapted polynomial maximization method for finding the estimates of scalar parameter of statistically dependent non-Gaussian random quantities is given. It is shown that using the correlation measures to describe statistically dependent random sequences allows to adapt the polynomial maximization method for the case of correlated quantities. The type of stochastic polynomial, on which the correlated random sequence is distributed, according to the polynomial maximization method, is formed taking into account correlations

Using the polynomial maximization method, adapted to the correlation case for estimating the scalar parameter of asymmetric correlated random quantity is shown in the paper. It is shown that the variance of the obtained estimates at constant values of the sample volume is smaller than the variance of the estimates, obtained using the polynomial maximization method, unadapted on the correlation case. It should also be noted that taking into account the non-Gaussianity of the studied quantities in polynomial maximization method algorithms allows to obtain estimates with the best probabilistic features compared with classical algorithms of the method of moments.

Author Biographies

Владимир Васильевич Палагин, Cherkasy State Technological University bul. Shevchenko 460, Cherkasy, Ukraine, 18006

Ph.D,

Department of Radio Engineering

Александр Витальевич Ивченко, Cherkasy State Technological University bul. Shevchenko 460, Cherkasy, Ukraine, 18006

Assistant

Department of Radio Engineering

References

  1. Андерсон, Т. Введение в многомерный статистический анализ [Текст] / Т. Андерсон – М.: Государственное издательство физико-математической литературы, 1963. – 500 с.
  2. Бендат, Дж. Прикладной анализ случайных данных [Текст] / Дж. Бендат, А. Пирсон – М.: Мир, 1989. – 540 с.
  3. Van Trees, H. L. Detection, Estimation, and Modulation Theory [Тext] / H. L. Van Trees // John Wiley. - 2002. - 1470 c.
  4. Hayes, M. H. Statistical Digital Signal Processing and Modeling [Тext] / M. H. Hayes // New York: John Wiley & Sons. - 1996. - 330 c.
  5. Kay, S. Fundamentals of Statistical Signal Processing: Estimation Theory [Тext] / S. Kay // Englewood Cliffs, N. J. - 1993. – 326c.
  6. Tuzlukov, V. P. Signal Processing Noise [Тext] / V. P. Tuzlukov // CRC Press/ - 2002. - 676 c.
  7. Huang, W. N. Steady creep bending in a beam with random material parameters [Тext] / W. N. Huang, F. A. Cozzarelli // II J. Franklin Instit. - 1980. - Vol. 294, №5. - C. 323 - 337.
  8. Westlung, R. Properties of a random creep process [Тext] / R. Westlung // II Int. J. Solids and Structures. - 1982. - Vol. 18. №4. - C. 275 - 283.
  9. Соленов, В. И. Нелинейная обработка и адаптация в негауссовских помехах [Текст] / В. И. Соленов, О. И. Шелухин // Киев: КМУГА. - 1997. - 180 с.
  10. Kunchenko, Y. P. Polynomial Parameter Estimations of Close to Gaussian Random variables [Тext] / Y. P. Kunchenko // Germany, Aachen: Shaker Verlag, 2002. - 396 p.
  11. Палагин, В. В. Адаптация метода максимизации полинома для оценки параметров случайных величин по статистически-зависимой выборке [Текст] / В. В. Палагин, А. В. Ивченко // Сборник научных трудов «Системы обработки информации». Харьков. 2009.- Вып. 2(76).- С. 118-123.
  12. Палагин, В. В. Оценка параметра ассиметрии коррелированной негауссовской помехи методом максимизации полинома [Текст] / В. В. Палагин, А. В. Ивченко // Весник ЧГТУ. - 2009. - №2. - С.67-72.
  13. Anderson, Т. W. (1963). An introduction to multivariate statistical analysis. New York: John Wiley and Sons, Inc., 374.
  14. Bendat, J. S., Piersol, A. G. (1986). Analysis and Measurement Procedures 2nd edition. New York: John Wiley, 566.
  15. Van Trees, H. L. (2002). Detection, Estimation, and Modulation Theory. - Part IV: Optimum Array Processing. John Wiley, 1470.
  16. Hayes, M. H. (1996). Statistical Digital Signal Processing and Modeling. New York: John Wiley & Sons, 330.
  17. Kay, S. (1993). Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice Hall, Englewood Cliffs, N.J, 326.
  18. Tuzlukov, V. P. (2002). Signal Processing Noise. CRC Press, 676.
  19. Huang, W. N. (1980). Steady creep bending in a beam with random material parameters. Franklin Instit, Vol. 294, №5., 323 – 337.
  20. Westlung, R. (1982). Properties of a random creep process. IR. Westlung II Int. J. Solids and Structures, Vol. 18, №4, 275 - 283.
  21. Solenov, V. I., Shelukhin, O. I. (1997). Nonlinear processing and adaptation in non-Gaussian noise. Ukraine, Kiev: KMUGA, 180.
  22. Kunchenko, Y. P. (2002). Polynomial Parameter Estimations of Close to Gaussian Random variables. Germany, Aachen: Shaker Verlag, 396.
  23. Palagin, V. V., Ivchenko, A. V. (2009). Adapting the method of maximizing the polynomial to estimate the parameters of random variables are statistically dependent sample. Ukraine, Kharkiv: KhUAF, Systems of information processing., № 2(76), 118-123.
  24. Palagin V. V., Ivchenko A. V. (2009). Parameter Estimation of asymmetry correlated non-Gaussian noise by maximizing the polynomial. Bulletin of ChSTU №2, 67-72.

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Published

2014-02-12

How to Cite

Палагин, В. В., & Ивченко, А. В. (2014). The analysis of polynomial method on evaluation of parameter of correlated non-gaussian random quantity. Eastern-European Journal of Enterprise Technologies, 1(4(67), 29–33. https://doi.org/10.15587/1729-4061.2014.20023

Issue

Vol. 1 No. 4(67) (2014): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2014 Владимир Васильевич Палагин, Александр Витальевич Ивченко

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