方法对比

	加权最小二乘法 (WLS)	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	1935	1935
提出者	Alexander Craig Aitken	Alexander Craig Aitken
类型	Weighted linear estimator	Linear estimator
开创性文献	Aitken, A. C. (1935). IV.—On least squares and linear combination of observations. Proceedings of the Royal Society of Edinburgh, 55, 42–48.	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	WLS, weighted regression, heteroscedasticity-corrected OLS, variance-weighted least squares	GLS, Aitken estimator, EGLS, feasible GLS
相关	3	3
摘要	Weighted Least Squares is a generalization of Ordinary Least Squares (OLS) regression that assigns each observation a weight inversely proportional to its error variance, thereby down-weighting high-variance data points and up-weighting precise ones. Introduced in its general matrix form by Alexander Craig Aitken in 1935, WLS is the canonical remedy when heteroscedasticity is present and the error variance structure is known or can be reliably estimated.	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.