Methoden vergleichen

	Kleinste-Quadrate-Schätzung (OLS)	Verallgemeinerte Kleinste Quadrate (GLS)
Fachgebiet	Statistik	Statistik
Familie	Regression model	Regression model
Entstehungsjahr	1805	1935
Urheber	Adrien-Marie Legendre (1805); Carl Friedrich Gauss (1809)	Alexander Craig Aitken
Typ	Linear parameter estimation	Linear estimator
Wegweisende Quelle	Legendre, A.-M. (1805). Nouvelles méthodes pour la détermination des orbites des comètes. Firmin Didot, Paris. [Appendix: Sur la Méthode des moindres quarrés, pp. 72–80.]	Aitken, A. C. (1935). IV.—On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42–48.
Aliasnamen	OLS, OLS regression, linear least squares, classical linear regression	GLS, Aitken estimator, EGLS, feasible GLS
Verwandt	8	3
Zusammenfassung	Ordinary Least Squares (OLS) is the canonical method for estimating the parameters of a linear regression model by minimizing the sum of squared differences between observed and predicted values. First published by Adrien-Marie Legendre in 1805 and independently developed by Carl Friedrich Gauss (who claimed priority from 1795), OLS is provably optimal under the Gauss-Markov theorem: given its assumptions, it yields the Best Linear Unbiased Estimator (BLUE) of the regression coefficients.	Generalized Least Squares (GLS) is a linear regression estimator that extends ordinary least squares to handle situations where the error terms are correlated or have non-constant variance (heteroscedasticity). Introduced by Alexander Craig Aitken in 1935, GLS achieves the Best Linear Unbiased Estimator (BLUE) under a general error covariance structure by weighting observations according to their precision, providing a theoretical bridge between OLS and modern linear mixed models.