# EQUALITY OF LS AND AITKEN ESTIMATIONS OF THE HIGHER COEFFICIENT OF THE LINEAR REGRESSION MODEL IN THE CASE OF TRIDIAGONAL BISYMMETRIC COVARIANCE MATRIX

### Abstract

At the paper a linear regression model whose function has the form f(x) = ax + b, a and b — unknown parameters, is studied. Approximate values (observations) of functions f(x) are registered at equidistant points of a line segment. It is also assumed that the covariance matrix of deviations is a tridiagonal bisymmetric matrix. In the theorem proved in the paper, in the case of an odd number of observation points, a necessary and sufficient condition for the elements of this covariance matrix is found, which ensures the equality of the LS estimate and the Aitken estimate of the a parameter of this model. With this type of covariance matrix of deviations, the estimates of Aitken and LS of parameter b will not coincide.

### References

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Savkina M. Yu. Equality of least squares method and Aitken senior coefficient estimates of the linear regression model in the case of correlated deviations. Journal of Numerical and Applied Mathematics. 2021. No. 2 (136). P. 64-72. https://doi.org/10.17721/2706-9699.2021.2.06

Savkina M. The necessary condition for the coincidence of LS and Aitken estimates of the senior coefficient of the linear regression model in the case of correlated deviations. Journal of Numerical and Applied Mathematics. 2022. No 2. С. 116-125. https://doi.org/10.17721/2706-9699.2022.2.14

Savkina M.Yu. A necessary condition for the coincidence of the LS and Aitken estimates is in the case that the covariance matrix of deviations is a tridiagonal bisymmetric matrix. Collection of Scientific Papers of the XXVII All-Ukrainian Scientific Conference "Modern Problems of Applied Mathematics and Computer Sciences", Lviv, November 7–9, 2023. C. 194-196.