De theoretische zijde van de methode der kleinste kwadraten

The theoretical aspect of least squares. This article contains a slightly modified presentation of the Markoff theory of least squares as developed along different lines by Aitken and by David and Neyman. The modifications aim at a more complete treatment and a geometrical illustration of the connection between best linear estimates and generalized least squares. The unbiasedness of ordinary least squares estimates in the case of heteroscedastic and correlated errors is stressed and the loss of efficiency is shown to be generally small. Topics like orthogonalization, partial correlation and what is called "over-correlation" are treated in passing. Matrices are constantly used, being the adequate tools in this matter. In the appendix a special relevant matrix theorem is derived, viz. a generalization of the well known Cauchy inequality.