Methoden vergleichen

	Gewichtete Kleinste Quadrate (GKS)	Verallgemeinerte Kleinste Quadrate (GLS)
Fachgebiet	Statistik	Statistik
Familie	Regression model	Regression model
Entstehungsjahr	1935	1935
Urheber	Alexander Craig Aitken	Alexander Craig Aitken
Typ	Weighted linear estimator	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.	Aitken, A. C. (1935). IV.—On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42–48.
Aliasnamen	WLS, weighted regression, heteroscedasticity-corrected OLS, variance-weighted least squares	GLS, Aitken estimator, EGLS, feasible GLS
Verwandt	3	3
Zusammenfassung	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.	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.