手法を比較

	頑健な重回帰分析	頑健回帰
分野	統計学	統計学
系統	Regression model	Regression model
提唱年	1964–1980s	1964
提唱者	Peter J. Huber (M-estimators, 1964); extended by Rousseeuw, Yohai, and Maronna	Peter J. Huber (M-estimation, 1964); Frank Hampel (influence function, 1974)
種類	Robust linear regression	Regression with outlier resistance
原典	Huber, P. J. (1964). Robust estimation of a location parameter. Annals of Mathematical Statistics, 35(1), 73–101.	Huber, P. J. (1964). Robust estimation of a location parameter. The Annals of Mathematical Statistics, 35(1), 73–101.
別名	robust MLR, M-estimator regression, resistant multiple regression, robust OLS	M-estimation regression, robust linear regression, outlier-resistant regression, MM-estimation
関連	6	6
概要	Robust multiple linear regression estimates the linear relationship between a continuous outcome and several predictors while being resistant to outliers and violations of the normality assumption. Instead of minimising the sum of squared residuals, it uses a bounded loss function — most commonly Huber's or Tukey's bisquare — so that extreme observations receive limited influence on the estimated 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.