Σύγκριση μεθόδων

	S-εκτιμητής για στιβαρή παλινδρόμηση	Εκτίμηση MM για Ανθεκτική Παλινδρόμηση	Παλινδρόμηση Ποσοστημορίων	Εκτιμητής Τ (τ) Παλινδρόμησης
Πεδίο	Στατιστική	Στατιστική	Οικονομετρία	Στατιστική
Οικογένεια	Regression model	Regression model	Regression model	Regression model
Έτος προέλευσης	1984	1987	1978	1988
Δημιουργός	Rousseeuw & Yohai (1984)	Victor J. Yohai	Koenker & Bassett	Yohai & Zamar
Τύπος	Robust linear regression	Robust linear regression	Conditional quantile regression	Robust linear regression
Θεμελιώδης πηγή	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.	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.
Εναλλακτικές ονομασίες	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	tau regression estimator, robust tau regression, Tau-Tahmin Edici
Συναφείς	5	5	5	4
Σύνοψη	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.	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.