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Application of the Polynomial Maximization Method for Estimation Parameters in the Polynomial Regression with Non-Gaussian Residuals

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Automation 2021: Recent Achievements in Automation, Robotics and Measurement Techniques (AUTOMATION 2021)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1390))

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Abstract

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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Author information

Authors and Affiliations

  1. Cherkasy State Business College, Cherkasy, Ukraine

    Serhii Zabolotnii & Oleksandr Tkachenko

  2. Kyiv National University of Technologies and Design, Kiev, Ukraine

    Serhii Zabolotnii

  3. Łukasiewicz Research Network – Industrial Research Institute of Automation and Measurements PIAP, Al. Jerozolimskie 202, 02-486, Warszawa, Poland

    Zygmunt Lech Warsza

Authors
  1. Serhii Zabolotnii
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  2. Oleksandr Tkachenko
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  3. Zygmunt Lech Warsza
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Corresponding author

Correspondence to Serhii Zabolotnii .

Editor information

Editors and Affiliations

  1. ŁUKASIEWICZ Research Network, Industrial Research Institute for Automation and Measurements PIAP, Warsaw, Poland

    Roman Szewczyk

  2. ŁUKASIEWICZ Research Network, Industrial Research Institute for Automation and Measurements PIAP, Warsaw, Poland

    Cezary Zieliński

  3. ŁUKASIEWICZ Research Network, Industrial Research Institute for Automation and Measurements PIAP, Warsaw, Poland

    Małgorzata Kaliczyńska

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Zabolotnii, S., Tkachenko, O., Warsza, Z.L. (2021). Application of the Polynomial Maximization Method for Estimation Parameters in the Polynomial Regression with Non-Gaussian Residuals. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds) Automation 2021: Recent Achievements in Automation, Robotics and Measurement Techniques. AUTOMATION 2021. Advances in Intelligent Systems and Computing, vol 1390. Springer, Cham. https://doi.org/10.1007/978-3-030-74893-7_36

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