手法を比較

	加重最小二乗法 (WLS)	一般化最小二乗法 (GLS)
分野	統計学	統計学
系統	Regression model	Regression model
提唱年	1935	1935
提唱者	Alexander Craig Aitken	Alexander Craig Aitken
種類	Weighted linear estimator	Linear estimator
原典	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.
別名	WLS, weighted regression, heteroscedasticity-corrected OLS, variance-weighted least squares	GLS, Aitken estimator, EGLS, feasible GLS
関連	3	3
概要	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.