手法を比較

	最小二乗法（OLS）	頑健回帰
分野	統計学	統計学
系統	Regression model	Regression model
提唱年	1805	1964
提唱者	Adrien-Marie Legendre (1805); Carl Friedrich Gauss (1809)	Peter J. Huber (M-estimation, 1964); Frank Hampel (influence function, 1974)
種類	Linear parameter estimation	Regression with outlier resistance
原典	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.]	Huber, P. J. (1964). Robust estimation of a location parameter. The Annals of Mathematical Statistics, 35(1), 73–101.
別名	OLS, OLS regression, linear least squares, classical linear regression	M-estimation regression, robust linear regression, outlier-resistant regression, MM-estimation
関連	8	6
概要	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.	Robust regression estimates the linear relationship between a continuous outcome and predictors while sharply reducing the influence of outliers and leverage points. Unlike OLS, which is highly sensitive to extreme observations, robust methods assign down-weighted influence to atypical data points, producing coefficient estimates that remain stable even when a fraction of the data is contaminated or non-normally distributed.