Матеріали науково-практичних конференцій

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Browsing Матеріали науково-практичних конференцій by Subject "MATHEMATICS"

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    Application of the Polynomial Maximization Method for Estimating Nonlinear Regression Parameters with Non-Gaussian Asymmetric Errors
    (Springer Nature, 2024) Заболотній, Сергій Васильович; Zabolotnii, Serhii; Tkachenko, Oleksandr; Nowakowski, Waldemar; Warsza, Zygmunt Lech
    In the article, an alternative approach to estimating parameters in nonlinear regression models under asymmetric error distributions is examined. A novel approach for adaptive estimation is proposed, which is based on the use of second-order polynomial functions. This enables a straightforward implementation to account for deviations from Gaussian idealization in the form of moments up to the fourth order. It is demonstrated that the overall problem can algorithmically be reduced to the numerical solution of a system of nonlinear stochastic equations. Analytical expressions are obtained, which facilitate the estimation of parameters and the analysis of their asymptotic variance. Statistical modeling using the Monte Carlo method was conducted, and the results indicate that the accuracy of PMM2 estimates is comparable to SLS estimates and significantly so exceeds the accuracy of OLS estimates.
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    Polynomial Estimation of Linear Regression Parameters for the Asymmetric PDF of Errors
    (Springer Nature, 2018) Zabolotnii, Serhii; Заболотній, Сергій Васильович; Warsza, Zygmunt Lech; Tkachenko, Oleksandr; Ткаченко, Олександр Миколайович
    This paper presents a non-standard way of finding estimates of linear regression parameters for the case of asymmetrically distributed errors. This approach is based on the polynomial maximization method (PMM) and uses the moment and cumulant description of random variables. Analytic expressions are obtained that allow one to find estimates and analyze their accuracy for the degree of the polynomial S = 1 and S = 2. It is shown that the variance of polynomial estimates (for S = 2) in the general case is less than the variance of estimates of the ordinary least squares method, which is a particular case of the polynomial maximization method (for S = 1). The increase in accuracy depends on the values of cumulant coefficients of higher orders of random errors of regression. Statistical modeling (Monte Carlo & bootstrapping method) is performed, the results of which confirm the effectiveness of the proposed approach.