方法对比

	普通最小二乘法 (OLS)	广义最小二乘法 (GLS)
领域	统计学	统计学
方法族	Regression model	Regression model
起源年份	1805	1935
提出者	Adrien-Marie Legendre (1805); Carl Friedrich Gauss (1809)	Alexander Craig Aitken
类型	Linear parameter estimation	Linear estimator
开创性文献	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.]	Aitken, A. C. (1935). IV.—On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42–48.
别名	OLS, OLS regression, linear least squares, classical linear regression	GLS, Aitken estimator, EGLS, feasible GLS
相关	8	3
摘要	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.