Сравнение на методи

	S-оценка за робастна регресия	MM-оценка за робастна регресия	Метод на най-малките квадрати (МНК)	Оценъчен метод Тау (τ) за регресия
Област	Статистика	Статистика	Иконометрия	Статистика
Семейство	Regression model	Regression model	Regression model	Regression model
Година на възникване	1984	1987	2019	1988
Създател	Rousseeuw & Yohai (1984)	Victor J. Yohai	Wooldridge (textbook treatment); classical least squares	Yohai & Zamar
Тип	Robust linear regression	Robust linear regression	Linear regression	Robust linear regression
Основополагащ източник	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.	Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860	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.
Други названия	S-estimation, robust S-regression, S-Tahmin Edici	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	tau regression estimator, robust tau regression, Tau-Tahmin Edici
Свързани	5	5	5	4
Резюме	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.	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 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.