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	S-skattare för robust regression	MM-estimering för robust regression	Tau-estimatorn för regression
Ämnesområde	Statistik	Statistik	Statistik
Familj	Regression model	Regression model	Regression model
Ursprungsår	1984	1987	1988
Upphovsperson	Rousseeuw & Yohai (1984)	Victor J. Yohai	Yohai & Zamar
Typ	Robust linear regression	Robust linear regression	Robust linear regression
Ursprungskälla	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.	Yohai, V. J. (1987). High Breakdown-Point and High Efficiency Robust Estimates for Regression. Annals of Statistics, 15(2), 642-656.	Yohai, V. J., & Zamar, R. H. (1988). High Breakdown-Point Estimates of Regression by Means of the Minimization of an Efficient Scale. Journal of the American Statistical Association, 83(402), 406-413.
Alias	S-estimation, robust S-regression, S-Tahmin Edici	MM-estimation, MM robust regression, high-breakdown high-efficiency estimator, MM-Tahmin Edici	tau regression estimator, robust tau regression, Tau-Tahmin Edici
Närliggande	5	5	4
Sammanfattning	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.	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 Tau estimator is a robust linear regression method introduced by Yohai and Zamar in 1988 that fits the model by minimising an efficient τ-scale of the residuals. It builds on the scale estimate of the S-estimator to combine a high breakdown point with high statistical efficiency, and is often used as an alternative to the MM-estimator in small samples.