We investigate the properties of multiple linear regression estimators obtained by the Ordinary Least Squares method (OLS) and the Generalized Least Squares method (GLS, Aitken estimator) assuming substantially different errors in input data. We illustrate the mechanism that leads to fallacious conclusions about the quality of OLS and Aitken estimators based on visual graphical analysis of experimental data. Numerical simulation and comparative analysis of the estimators is carried out for simple and parabolic regression models.
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References
G. Seber, Linear Regression Analysis [Russian translation], Mir, Moscow (1980).
C. R. Rao, Linear Statistical Inference and Its Applications [Russian translation], Nauka, Moscow (1968).
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Translated from Prikladnaya Matematika i Informatika, No. 51, 2016, pp. 95–99.
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Belov, A.G. Equality of OLS and Aitken Estimators. Comput Math Model 28, 74–77 (2017). https://doi.org/10.1007/s10598-016-9346-x
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DOI: https://doi.org/10.1007/s10598-016-9346-x