Інформаційні технології

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Browsing Інформаційні технології by Author "Chepynoha, Anatolii"

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    Estimating parameters of linear regression with an exponential power distribution of errors by using a polynomial maximization method
    (ПП «ТЕХНОЛОГІЧНИЙ ЦЕНТР», Український державний університет залізничного транспорту, 2021) Заболотній, Сергій Васильович; Zabolotnii, Serhii; Хотунов, Владислав Ігорович; Khotunov, Vladyslav; Чепинога, Анатолій Володимирович; Chepynoha, Anatolii; Ткаченко, Олександр Миколайович; Tkachenko, Oleksandr
    This 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.
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    Сomparative Analysis of Polynomial Maximization and Maximum Likelihood Estimates for Data with Exponential Power Distribution
    (Національний технічний університет України «Київський політехнічний інститут імені Ігоря Сікорського», 2020) Zabolotnii, Serhii; Заболотній, Сергій Васильович; Chepynoha, Anatolii; Чепинога, Анатолій Володимирович; Chorniy, Andriy; Чорній, Андрій Михайлович; Honcharov, Artem; Гончаров, Артем Володимирович
    The work is devoted to the estimate accuracy comparative analysis of the experimental data parameters with exponential power distribution (EPD) using the classical Maximum Likelihood Estimation (MLE) and the original Polynomial Maximization Method (PMM). In contrast to the parametric approach of MLE, which uses the description in the form of probability density distribution, PMM is based on a partial description in the of higher-order statistics form and the mathematical apparatus of Kunchenko's stochastic polynomials. An algorithm for finding PMM estimates using 3rd order stochastic polynomials is presented. Analytical expressions allowing to determine the variance of PMM-estimates of the asymptotic case parameters and EPD parameters with a priori information are obtained. It is shown that the relative theoretical estimates accuracy of different methods significantly depends on the EPD shape parameter and matches only for a separate case of Gaussian distribution. The effectiveness of different approaches (including valuation of mean values estimates) both with and without a priori information on EPD properties was investigated by repeated statistical tests (through Monte Carlo Method). The greatest efficiency areas for each of methods depending on EPD shape parameter and sample data volume are constructed.