Methoden vergleichen

	Nichtlineare gewichtete Kleinste Quadrate (NWLS)	Verallgemeinerte Kleinste Quadrate (GLS)	Methode der kleinsten Quadrate (OLS)
Fachgebiet	Ökonometrie	Statistik	Ökonometrie
Familie	Regression model	Regression model	Regression model
Entstehungsjahr	1960s–1980s (formalized in applied econometrics)	1935	2019
Urheber	Extension of Gauss-Newton nonlinear least squares with Aitken-type weighting	Alexander Craig Aitken	Wooldridge (textbook treatment); classical least squares
Typ	Nonlinear regression estimator	Linear estimator	Linear regression
Wegweisende Quelle	Greene, W. H. (2018). Econometric Analysis (8th ed.). Pearson Education. ISBN: 978-0134461366	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
Aliasnamen	NWLS, nonlinear weighted least squares, weighted nonlinear regression, heteroscedasticity-corrected nonlinear regression	GLS, Aitken estimator, EGLS, feasible GLS	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu
Verwandt	3	3	5
Zusammenfassung	Nonlinear Weighted Least Squares combines the flexibility of nonlinear regression with the variance-stabilizing power of observation-level weights. It minimises a weighted sum of squared residuals around a user-specified nonlinear mean function, making it the method of choice when the relationship is inherently nonlinear and error variance differs across observations.	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).