Vertaile menetelmiä

	W-estimaattorin robusti regressio (Welsch / Tukey Bisquare)	S-estimaattori robustissa regressiossa	Theil-Senin estimaattori
Tieteenala	Tilastotiede	Tilastotiede	Tilastotiede
Menetelmäperhe	Regression model	Regression model	Regression model
Syntyvuosi	1974	1984	1968
Kehittäjä	Beaton & Tukey (bisquare weight); Welsch (Welsch weight)	Rousseeuw & Yohai (1984)	Henri Theil (1950); P. K. Sen (1968)
Tyyppi	Robust regression (redescending M-estimator)	Robust linear regression	Robust linear regression
Alkuperäislähde	Beaton, A. E. & Tukey, J. W. (1974). The Fitting of Power Series, Meaning Polynomials, Illustrated on Band-Spectroscopic Data. Technometrics, 16(2), 147-185.	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.
Rinnakkaisnimet	Tukey bisquare M-estimator, Welsch M-estimator, redescending M-estimator, W-Tahmin Edici (Welsch / Tukey Bisquare)	S-estimation, robust S-regression, S-Tahmin Edici	Theil-Sen Tahmincisi, Theil-Sen regression, median slope estimator, Sen's slope estimator
Liittyvät	4	5	6
Tiivistelmä	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.	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%.