Рівність оцінок МНК та Ейткена параметра лінійної моделі регресії, коли коваріаційна матриця відхилень є симетричною матрицею Тепліца загального вигляду
In this paper, we study a regression model whose function has the form  f(x)=ax+b, where a and  b - unknown parameters, and the covariance matrix of deviations is a symmetric Toeplitz matrix of the general form. Approximate values (obs...
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| Date: | 2023 |
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| Main Author: | |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України
2023
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| Subjects: | |
| Online Access: | https://www.fmmit.lviv.ua/index.php/fmmit/article/view/314 |
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| Journal Title: | Physico-mathematical modeling and informational technologies |
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Physico-mathematical modeling and informational technologies| Summary: | In this paper, we study a regression model whose function has the form  f(x)=ax+b, where a and  b - unknown parameters, and the covariance matrix of deviations is a symmetric Toeplitz matrix of the general form. Approximate values (observations) of the function f(x) are recorded at equidistant points of the segment [0;1]. The paper presents a theorem that gives a necessary and sufficient condition for the elements of the covariance matrix of deviations of the specified form for the coincidence of the MNK estimation and the Aitken estimation of the parameter a of such model. |
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