手法を比較

	ロバスト単回帰分析	加重最小二乗法 (WLS)
分野	統計学	統計学
系統	Regression model	Regression model
提唱年	1964-1987	1935
提唱者	Peter J. Huber (M-estimators, 1964); Rousseeuw & Leroy (practical framework, 1987)	Alexander Craig Aitken
種類	Robust linear regression	Weighted linear estimator
原典	Rousseeuw, P. J., & Leroy, A. M. (1987). Robust Regression and Outlier Detection. John Wiley & Sons. ISBN: 978-0471852339	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	robust SLR, M-estimator simple regression, outlier-resistant simple regression, robust bivariate regression	WLS, weighted regression, heteroscedasticity-corrected OLS, variance-weighted least squares
関連	6	3
概要	Robust simple linear regression fits a straight line through bivariate data using loss functions or weighting schemes that down-weight outliers, producing slope and intercept estimates that are far less sensitive to extreme observations than ordinary least squares while remaining easy to interpret.	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.