Vertaile menetelmiä

	Yleistetty pienimmän neliösumman menetelmä (GLS)	OLS-regressio (Ordinary Least Squares)	Robust OLS (OLS, jossa robustit keskivirheet)
Tieteenala	Tilastotiede	Ekonometria	Ekonometria
Menetelmäperhe	Regression model	Regression model	Regression model
Syntyvuosi	1935	2019	1980
Kehittäjä	Alexander Craig Aitken	Wooldridge (textbook treatment); classical least squares	Halbert White
Tyyppi	Linear estimator	Linear regression	Linear regression with robust inference
Alkuperäislähde	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	White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica, 48(4), 817–838.
Rinnakkaisnimet	GLS, Aitken estimator, EGLS, feasible GLS	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu	HC robust regression, White robust OLS, sandwich estimator OLS, OLS with robust standard errors
Liittyvät	3	5	6
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.	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).	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.