Linganisha mbinu
Pitia mbinu ulizochagua bega kwa bega; safu zinazotofautiana zinaangaziwa.
| Mbinu ya Viwango Vidogo Vilivyopanuliwa (GLS)× | Ordinary Least Squares (OLS)× | |
|---|---|---|
| Nyanja | Takwimu | Takwimu |
| Familia | Regression model | Regression model |
| Mwaka wa asili≠ | 1935 | 1805 |
| Mwanzilishi≠ | Alexander Craig Aitken | Adrien-Marie Legendre (1805); Carl Friedrich Gauss (1809) |
| Aina≠ | Linear estimator | Linear parameter estimation |
| Chanzo asilia≠ | Aitken, A. C. (1935). IV.—On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42–48. DOI ↗ | 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 ↗ |
| Majina mbadala≠ | GLS, Aitken estimator, EGLS, feasible GLS | OLS, OLS regression, linear least squares, classical linear regression |
| Zinazohusiana≠ | 3 | 8 |
| Muhtasari≠ | 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 (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. |
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