Матеріали науково-практичних конференцій

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Browsing Матеріали науково-практичних конференцій by Subject "SOCIAL SCIENCES::Statistics, computer and systems science"

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    Application of the Polynomial Maximization Method for Estimation Parameters in the Polynomial Regression with Non-Gaussian Advances in Intelligent Systems and Computing
    (Springer Nature, 2021) Zabolotnii, Serhii; Заболотній, Сергій Васильович; Tkachenko, Oleksandr; Ткаченко, Олександр Миколайович; Warsza, Zygmunt Lech
    This paper considers the application of the polynomial maximization method to find estimates of the parameters of polynomial regression. It is shown that this method can be effective for the case when the distribution of the random component of the regression models differs significantly from the Gaussian distribution. This approach is adaptive and is based on the analysis of higher-order statistics of regression residuals. Analytical expressions that allow finding estimates and analyzing their uncertainty are obtained. Cases of asymmetry and symmetry of the distribution of regression errors are considered. It is shown that the variance of estimates of the polynomial maximization method can be significantly less than the variance of the estimates of the least squares method, which is a special case. The increase in accuracy depends on the values of the cumulant coefficients of higher orders of random errors of the regression model. The results of statistical modeling by the Monte Carlo method confirm the effectiveness of the proposed approach.
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    Estimation of Linear Regression Parameters of Symmetric Non-Gaussian Errors by Polynomial Maximization Method
    (Springer Nature, 2019) Zabolotnii, Serhii; Заболотній, Сергій Васильович; Warsza, Zygmunt Lech; Tkachenko, Oleksandr; Ткаченко, Олександр Миколайович
    In this paper, a new way of estimation of single-factor linear regression parameters of symmetrically distributed non-Gaussian errors is proposed. This new approach is based on the Polynomial Maximization Method (PMM) and uses the description of random variables by higher order statistics (moments and cumulants). Analytic expressions that allow to find estimates and analyze their asymptotic accuracy are obtained for the degree of polynomial S = 3. It is shown that the variance of polynomial estimates can be less than the variance of estimates of the ordinary least squares’ method. The increase of accuracy depends on the values of cumulant coefficients of higher order of the random regression errors. The statistical modeling of the Monte Carlo method has been performed. The results confirm the effectiveness of the proposed approach.
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    Estimation of Measurand Parameters for Data from Asymmetric Distributions by Polynomial Maximization Method
    (Springer Nature, 2018) Warsza, Zygmunt Lech; Zabolotnii, Serhii; Заболотній, Сергій Васильович
    In this paper the non-conventional method for evaluating the standard uncertainty of the estimator of measurand value obtained from the non-Gaussian asymmetrically distributed sampled data with a priori partial description (known only few initial moments, unknown PDF distribution of population) is proposed. This method of statistical estimation is based on the apparatus of maximization the stochastic polynomials (PMM method proposed by Kunchenko) and uses the higher-order statistics (moment or cumulant description) of random variables. The analytical expressions for finding estimates and analyzing their accuracy to the degree of the polynomial s = 2 is given. It is shown that for the asymmetric PDF-s the uncertainty estimates for received polynomial are generally smaller than the uncertainty estimates obtained based on the mean (arithmetic average). Reducing the uncertainty of measurement depends on the skewness and kurtosis. On the basis of the Monte Carlo method statistical modelling is carried out, the results confirm the effectiveness of the proposed approach.
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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.