Σύγκριση μεθόδων

	Εκτιμητής W (Welsch / Tukey Bisquare)	Παλινδρόμηση Ελαχίστων Τετραγώνων (OLS)	S-εκτιμητής για στιβαρή παλινδρόμηση
Πεδίο	Στατιστική	Οικονομετρία	Στατιστική
Οικογένεια	Regression model	Regression model	Regression model
Έτος προέλευσης	1974	2019	1984
Δημιουργός	Beaton & Tukey (bisquare weight); Welsch (Welsch weight)	Wooldridge (textbook treatment); classical least squares	Rousseeuw & Yohai (1984)
Τύπος	Robust regression (redescending M-estimator)	Linear regression	Robust linear regression
Θεμελιώδης πηγή	Beaton, A. E. & Tukey, J. W. (1974). The Fitting of Power Series, Meaning Polynomials, Illustrated on Band-Spectroscopic Data. Technometrics, 16(2), 147-185.	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.
Εναλλακτικές ονομασίες	Tukey bisquare M-estimator, Welsch M-estimator, redescending M-estimator, W-Tahmin Edici (Welsch / Tukey Bisquare)	ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu	S-estimation, robust S-regression, S-Tahmin Edici
Συναφείς	4	5	5
Σύνοψη	The W-estimator is a family of robust M-estimator variants for linear regression that use the Tukey bisquare and Welsch weight functions, introduced in the line of work going back to Beaton and Tukey (1974). Because its weights fall rapidly toward zero as a residual grows, it resists outliers more strongly than the Huber M-estimator.	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.