Vertaile menetelmiä

	Yleistetty pienimmän neliösumman menetelmä (GLS)	Painotettu pienimmän neliösumman menetelmä (WLS)
Tieteenala	Tilastotiede	Tilastotiede
Menetelmäperhe	Regression model	Regression model
Syntyvuosi	1935	1935
Kehittäjä	Alexander Craig Aitken	Alexander Craig Aitken
Tyyppi	Linear estimator	Weighted linear estimator
Alkuperäislähde	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.
Rinnakkaisnimet	GLS, Aitken estimator, EGLS, feasible GLS	WLS, weighted regression, heteroscedasticity-corrected OLS, variance-weighted least squares
Liittyvät	3	3
Tiivistelmä	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.	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.