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| Zwykła metoda najmniejszych kwadratów (OLS)× | Metoda najmniejszych kwadratów uogólnionych (GLS)× | |
|---|---|---|
| Dziedzina | Statystyka | Statystyka |
| Rodzina | Regression model | Regression model |
| Rok powstania≠ | 1805 | 1935 |
| Twórca≠ | Adrien-Marie Legendre (1805); Carl Friedrich Gauss (1809) | Alexander Craig Aitken |
| Typ≠ | Linear parameter estimation | Linear estimator |
| Źródło pierwotne≠ | Legendre, A.-M. (1805). Nouvelles méthodes pour la détermination des orbites des comètes. Firmin Didot, Paris. [Appendix: Sur la Méthode des moindres quarrés, pp. 72–80.] link ↗ | Aitken, A. C. (1935). IV.—On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42–48. DOI ↗ |
| Inne nazwy≠ | OLS, OLS regression, linear least squares, classical linear regression | GLS, Aitken estimator, EGLS, feasible GLS |
| Pokrewne≠ | 8 | 3 |
| Podsumowanie≠ | Ordinary Least Squares (OLS) is the canonical method for estimating the parameters of a linear regression model by minimizing the sum of squared differences between observed and predicted values. First published by Adrien-Marie Legendre in 1805 and independently developed by Carl Friedrich Gauss (who claimed priority from 1795), OLS is provably optimal under the Gauss-Markov theorem: given its assumptions, it yields the Best Linear Unbiased Estimator (BLUE) of the regression coefficients. | 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. |
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