Theorem about the sufficient condition for the equality of the estimates of the OLS and Aitken of the leading coefficient of quadratic regression

Fìz.-mat. model. ìnf. tehnol. 2021, 33:138-142

Abstract

At the paper in the case of heteroscedastic independent deviations a quadratic regression model is studied. A theorem is formulated that gives a sufficient condition on the variance of deviations for the coincidence of Aitken's estimate of the leading regression coefficient with his estimation of the OLS in the case of an odd number of observation points and a bisymmetric covariance matrix. On the basis of this theorem, in some cases examples of non-unit covariance matrices are constructed for which the indicated estimations of the leading coefficient of the quadratic regression coindcide.

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