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	S-skattare för robust regression	MM-estimering för robust regression	Kvantilregression
Ämnesområde	Statistik	Statistik	Ekonometri
Familj	Regression model	Regression model	Regression model
Ursprungsår	1984	1987	1978
Upphovsperson	Rousseeuw & Yohai (1984)	Victor J. Yohai	Koenker & Bassett
Typ	Robust linear regression	Robust linear regression	Conditional quantile 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.	Koenker, R. & Bassett, G., Jr. (1978). Regression Quantiles. Econometrica, 46(1), 33-50.
Alias	S-estimation, robust S-regression, S-Tahmin Edici	MM-estimation, MM robust regression, high-breakdown high-efficiency estimator, MM-Tahmin Edici	conditional quantile regression, regression quantiles, Kantil Regresyon
Närliggande	5	5	5
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.	Quantile regression models conditional quantiles of an outcome - the median, the 25th or 75th percentile, and so on - rather than the conditional mean that OLS targets. Introduced by Koenker and Bassett in 1978, it reveals how predictors act across the whole distribution, including its tails.