Σύγκριση μεθόδων

	Εκτίμηση MM για Ανθεκτική Παλινδρόμηση	Παλινδρόμηση Ελαχίστων Τετραγώνων (OLS)	S-εκτιμητής για στιβαρή παλινδρόμηση	Εκτιμητής Theil-Sen
Πεδίο	Στατιστική	Οικονομετρία	Στατιστική	Στατιστική
Οικογένεια	Regression model	Regression model	Regression model	Regression model
Έτος προέλευσης	1987	2019	1984	1968
Δημιουργός	Victor J. Yohai	Wooldridge (textbook treatment); classical least squares	Rousseeuw & Yohai (1984)	Henri Theil (1950); P. K. Sen (1968)
Τύπος	Robust linear regression	Linear regression	Robust linear regression	Robust linear regression
Θεμελιώδης πηγή	Yohai, V. J. (1987). High Breakdown-Point and High Efficiency Robust Estimates for Regression. Annals of Statistics, 15(2), 642-656.	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860	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.	Sen, P. K. (1968). Estimates of the Regression Coefficient Based on Kendall's Tau. Journal of the American Statistical Association, 63(324), 1379-1389.
Εναλλακτικές ονομασίες	MM-estimation, MM robust regression, high-breakdown high-efficiency estimator, MM-Tahmin Edici	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu	S-estimation, robust S-regression, S-Tahmin Edici	Theil-Sen Tahmincisi, Theil-Sen regression, median slope estimator, Sen's slope estimator
Συναφείς	5	5	5	6
Σύνοψη	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.	Ordinary Least Squares is the classical linear regression method that explains a continuous outcome as a linear combination of predictors. It estimates the coefficients by minimising the sum of squared residuals, and under the Gauss-Markov assumptions these estimates are the best linear unbiased estimator (BLUE).	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 Theil-Sen estimator is a robust linear regression method that estimates the slope as the median of the slopes computed over all pairs of data points. Introduced by Henri Theil in 1950 and extended by P. K. Sen in 1968, it tolerates outliers in the response with a breakdown point of about 29%.