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.