Vertaile menetelmiä

	Yleistetty pienimmän neliösumman menetelmä (GLS)	OLS-regressio (Ordinary Least Squares)	Paneeli yleistetty pienimmän neliösumman menetelmä (Paneeli GLS)	Robust OLS (OLS, jossa robustit keskivirheet)
Tieteenala	Tilastotiede	Ekonometria	Ekonometria	Ekonometria
Menetelmäperhe	Regression model	Regression model	Regression model	Regression model
Syntyvuosi	1935	2019	1935 / developed for panels 1980s–1990s	1980
Kehittäjä	Alexander Craig Aitken	Wooldridge (textbook treatment); classical least squares	Aitken (1935); extended to panel data by Baltagi and others	Halbert White
Tyyppi	Linear estimator	Linear regression	Generalized 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	Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data (2nd ed.). MIT Press. ISBN: 978-0262232586	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	Panel GLS, Generalized Least Squares for panel data, FGLS panel, feasible GLS panel	HC robust regression, White robust OLS, sandwich estimator OLS, OLS with robust standard errors
Liittyvät	3	5	3	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).	Panel GLS is a regression method for longitudinal data that explicitly models the non-spherical error structure — heteroscedasticity across units and serial correlation within units — to recover efficient coefficient estimates. Unlike OLS, it weights observations by the inverse of the error covariance matrix, yielding the Best Linear Unbiased Estimator when the error structure is correctly specified.	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.