Equality of MNK and Aitken estimations of the parameter of the linear regression model, when the covariance matrix of the deviations is a symmetric Toeplitz matrix of the general form

Abstract

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.