A Polynomial Estimation of Measurand Parameters for Samples of Non-Gaussian Symmetrically Distributed Data

Warsza, Z. L.; Zabolotnii, Serhii

doi:10.1007/978-3-319-54042-9_45

Cited by 9 publications

(3 citation statements)

References 4 publications

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“…However, in contrast to MLE, PMM uses not the density of distribution, but a simpler probabilistic description in the form of the final number of moments or cumulants to form such statistics. Note the functionality of PMM, which was successfully used to assess the shear of symmetrical [55][56][57] and asymmetrical [58] distributions, to determine the moment of changes (disorder) of the properties of random sequences in the a posteriori problem statement [59], and others. In particular, works [60,61] consider the use of cubic (at the power of polynomial S=3) modification of PMM to solve the problem of adaptive evaluation of the scalar parameter of experimental data acquired from EPD.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

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

Zabolotnii

Khotunov

Chepynoha

et al. 2021

EEJET

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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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Section: Literature Review and Problem Statementmentioning

confidence: 99%

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

Zabolotnii

Khotunov

Chepynoha

et al. 2021

EEJET

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show abstract

“…Zastosowanie metody maksymalizacji wielomianu stochastycznego PMM jako niekonwencjonalnego narzędzia matematycznego do wyznaczania parametrów wyniku pomiarów wielokrotnych o wartościach danych pobranych losowo z rozkładu symetrycznego autorzy omówili w [23]. Poniżej przedstawi się zastosowanie metody PMM dla próbek danych pomiarowych z rozkładów asymetrycznych.…”

Section: ʹɩ ƭǚ žřƞřȯ ǔ ȧřǜƭȧřǜ˿ƌ˘ȭ˿ ȧɂƞƭǚ ɡɂȧǔřʁɂ˹unclassified

“…Metodę tę można użyć w konstruowaniu algorytmów do wyznaczania nieliniowych estymatorów wartości i niepewności menzurandu dla danych pomiarowych rozproszonych losowo zarówno symetrycznie [23,24], jak i asymetrycznie oraz opisanych modelem niegaussowskim.…”

Section: ʕɩ ķȭǔɂʊǘǔ ǔ ƞřǚʊ˘ƭ ǘǔƭʁˁȭǘǔ ɡʁřƌunclassified

Estimation of measurand parameters for data from asymmetric distributions by polynomial maximization method (PMM)

Warsza

Zabolotnii

2018

PAR

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Estimation of Linear Regression Parameters of Symmetric Non-Gaussian Errors by Polynomial Maximization Method

Zabolotnii

Warsza

Tkachenko

2019

Advances in Intelligent Systems and Computing

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A Polynomial Estimation of Measurand Parameters for Samples of Non-Gaussian Symmetrically Distributed Data

Cited by 9 publications

References 4 publications

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

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

Estimation of measurand parameters for data from asymmetric distributions by polynomial maximization method (PMM)

Estimation of Linear Regression Parameters of Symmetric Non-Gaussian Errors by Polynomial Maximization Method

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