Methoden vergleichen

	Verallgemeinerte Kleinste Quadrate (GLS)	Methode der kleinsten Quadrate (OLS)	Gewichtete Kleinste Quadrate (GKS)
Fachgebiet	Statistik	Ökonometrie	Statistik
Familie	Regression model	Regression model	Regression model
Entstehungsjahr	1935	2019	1935
Urheber	Alexander Craig Aitken	Wooldridge (textbook treatment); classical least squares	Alexander Craig Aitken
Typ	Linear estimator	Linear regression	Weighted linear estimator
Wegweisende Quelle	Aitken, A. C. (1935). IV.—On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42–48.	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860	Aitken, A. C. (1935). IV.—On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42–48.
Aliasnamen	GLS, Aitken estimator, EGLS, feasible GLS	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu	WLS, weighted regression, heteroscedasticity-corrected OLS, variance-weighted least squares
Verwandt	3	5	3
Zusammenfassung	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.	Ordinary Least Squares is the classical linear regression method that explains a continuous outcome as a linear combination of predictors. It estimates the coefficients by minimising the sum of squared residuals, and under the Gauss-Markov assumptions these estimates are the best linear unbiased estimator (BLUE).	Weighted Least Squares is a generalization of Ordinary Least Squares (OLS) regression that assigns each observation a weight inversely proportional to its error variance, thereby down-weighting high-variance data points and up-weighting precise ones. Introduced in its general matrix form by Alexander Craig Aitken in 1935, WLS is the canonical remedy when heteroscedasticity is present and the error variance structure is known or can be reliably estimated.