Polynomial Estimation of Linear Regression Parameters for the Asymmetric PDF of Errors
| Autor: | Zygmunt L. Warsza, Oleksandr Tkachenko, Serhii W. Zabolotnii |
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| Rok vydání: | 2018 |
| Předmět: |
Polynomial
020209 energy 020208 electrical & electronic engineering 02 engineering and technology Maximization Moment (mathematics) Ordinary least squares Linear regression 0202 electrical engineering electronic engineering information engineering Kurtosis Applied mathematics Random variable Bootstrapping (statistics) Mathematics |
| Zdroj: | Advances in Intelligent Systems and Computing ISBN: 9783319771786 AUTOMATION |
| DOI: | 10.1007/978-3-319-77179-3_75 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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