Vertaile menetelmiä

	Robustit yleistetyt pienimmät neliöt (Robust GLS)	Yleistetty pienimmän neliösumman menetelmä (GLS)	Robust OLS (OLS, jossa robustit keskivirheet)
Tieteenala	Ekonometria	Tilastotiede	Ekonometria
Menetelmäperhe	Regression model	Regression model	Regression model
Syntyvuosi	1936 / 1980	1935	1980
Kehittäjä	Aitken (GLS theory, 1936); White (robust covariance, 1980)	Alexander Craig Aitken	Halbert White
Tyyppi	Robust linear regression	Linear estimator	Linear regression with robust inference
Alkuperäislähde	Greene, W. H. (2012). Econometric Analysis (7th ed.). Pearson. Chapter 9: The Generalized Regression Model and Heteroscedasticity. ISBN: 978-0131395381	Aitken, A. C. (1935). IV.—On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42–48.	White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica, 48(4), 817–838.
Rinnakkaisnimet	robust generalized least squares, GLS with robust standard errors, heteroscedasticity-consistent GLS, HC-GLS	GLS, Aitken estimator, EGLS, feasible GLS	HC robust regression, White robust OLS, sandwich estimator OLS, OLS with robust standard errors
Liittyvät	5	3	6
Tiivistelmä	Robust GLS extends classical Generalized Least Squares by pairing GLS coefficient estimation with heteroscedasticity- and autocorrelation-consistent (HAC) standard errors, or by using M-estimation within the GLS framework. It corrects for non-spherical errors — heteroscedasticity, autocorrelation, or both — while also guarding inference against misspecification of the error covariance structure.	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.	Robust OLS applies ordinary least squares to estimate coefficients and then replaces the classical standard errors with heteroscedasticity-consistent (HC) standard errors — commonly called White standard errors. This leaves the point estimates unchanged while yielding valid t-statistics and confidence intervals even when the error variance is not constant across observations.