Estimating parameters of linear regression with an exponential power distribution of errors by using a polynomial maximization method

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dc.contributor.authorЗаболотній, Сергій Васильович
dc.contributor.authorZabolotnii, Serhii
dc.contributor.authorХотунов, Владислав Ігорович
dc.contributor.authorKhotunov, Vladyslav
dc.contributor.authorЧепинога, Анатолій Володимирович
dc.contributor.authorChepynoha, Anatolii
dc.contributor.authorТкаченко, Олександр Миколайович
dc.contributor.authorTkachenko, Oleksandr
dc.date.accessioned2025-10-08T08:21:07Z
dc.date.available2025-10-08T08:21:07Z
dc.date.issued2021
dc.description.abstractThis paper considers the application of a method for maximizing polynomials in order to find estimates of the parameters of a multifactorial linear regression provided the random errors of the regression model follow an exponential power distribution. The method used is conceptually close to a maximum likelihood method because it is based on the maximization of selective statistics in the neighborhood of the true values of the evaluated parameters. However, in contrast to the classical parametric approach, it employs a partial probabilistic description in the form of a limited number of statistics of higher orders. The adaptive algorithm of statistical estimation has been synthesized, which takes into consideration the properties of regression residues and makes it possible to find refined values for the estimates of the parameters of a linear multifactorial regression using the numerical Newton-Rafson iterative procedure. Based on the apparatus of the quantity of extracted information, the analytical expressions have been derived that make it possible to analyze the theoretical accuracy (asymptotic variances) of estimates for the method of maximizing polynomials depending on the magnitude of the exponential power distribution parameters. Statistical modeling was employed to perform a comparative analysis of the variance of estimates obtained using the method of maximizing polynomials with the accuracy of classical methods: the least squares and maximum likelihood. Regions of the greatest efficiency for each studied method have been constructed, depending on the magnitude of the parameter of the form of exponential power distribution and sample size. It has been shown that estimates from the polynomial maximization method may demonstrate a much lower variance compared to the estimates from a least-square method. And, in some cases (for flat-topped distributions and in the absence of a priori information), may exceed the estimates from the maximum likelihood method in terms of accuracy.
dc.identifier.citationZabolotnii S.V., Khotunov V.I., Chepynoha A.V., Tkachenko O.M. Estimating parameters of linear regression with an exponential power distribution of errors by using a polynomial maximization method. Eastern-European Journal of Enterprise Technologies. 2021. № 1 (109) р. 64–73. DOI: https://doi.org/10.15587/1729-4061.2021.225525. [Scopus, квартиль Q 2]
dc.identifier.uriПП «ТЕХНОЛОГІЧНИЙ ЦЕНТР», Український державний університет залізничного транспорту
dc.identifier.urihttps://dr.csbc.edu.ua/handle/123456789/454
dc.language.isoen
dc.publisherПП «ТЕХНОЛОГІЧНИЙ ЦЕНТР», Український державний університет залізничного транспорту
dc.subjectSOCIAL SCIENCES::Statistics, computer and systems science::Informatics, computer and systems science::Informatics
dc.subjectSOCIAL SCIENCES::Statistics, computer and systems science::Informatics, computer and systems science::Information technology
dc.subjectSOCIAL SCIENCES::Statistics, computer and systems science::Informatics, computer and systems science
dc.subjectTECHNOLOGY
dc.titleEstimating parameters of linear regression with an exponential power distribution of errors by using a polynomial maximization method
dc.typeArticle
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