手法を比較

	MM推定によるロバスト回帰	ロバスト回帰のためのS推定量
分野	統計学	統計学
系統	Regression model	Regression model
提唱年	1987	1984
提唱者	Victor J. Yohai	Rousseeuw & Yohai (1984)
種類	Robust linear regression	Robust linear regression
原典	Yohai, V. J. (1987). High Breakdown-Point and High Efficiency Robust Estimates for Regression. Annals of Statistics, 15(2), 642-656.	Rousseeuw, P. J. & Yohai, V. J. (1984). Robust Regression by Means of S-Estimators. In Robust and Nonlinear Time Series Analysis (Lecture Notes in Statistics, Vol. 26, pp. 256-272). Springer.
別名	MM-estimation, MM robust regression, high-breakdown high-efficiency estimator, MM-Tahmin Edici	S-estimation, robust S-regression, S-Tahmin Edici
関連	5	5
概要	The MM-estimator is a robust linear regression method introduced by Victor J. Yohai in 1987. It combines the high breakdown point of an S-estimator with the high efficiency of an M-estimator, so it resists outliers strongly while still using the data efficiently when errors are well-behaved.	The S-estimator is a robust linear-regression method, introduced by Rousseeuw and Yohai in 1984, that estimates the coefficients by minimising a robust M-estimate of the residual scale rather than the variance of the residuals. By driving down a bounded measure of residual spread it can attain a breakdown point of up to 50%, so it stays reliable even when a large share of the data are outliers, and it provides the first stage of the well-known MM-estimator.