So sánh phương pháp

	Ước lượng W cho Hồi quy Mạnh mẽ (Welsch / Tukey Bisquare)	Ước lượng MM cho hồi quy vững mạnh	Ước lượng S cho hồi quy vững mạnh
Lĩnh vực	Thống kê	Thống kê	Thống kê
Họ	Regression model	Regression model	Regression model
Năm ra đời	1974	1987	1984
Người khởi xướng	Beaton & Tukey (bisquare weight); Welsch (Welsch weight)	Victor J. Yohai	Rousseeuw & Yohai (1984)
Loại	Robust regression (redescending M-estimator)	Robust linear regression	Robust linear regression
Công trình gốc	Beaton, A. E. & Tukey, J. W. (1974). The Fitting of Power Series, Meaning Polynomials, Illustrated on Band-Spectroscopic Data. Technometrics, 16(2), 147-185.	Yohai, V. J. (1987). High Breakdown-Point and High Efficiency Robust Estimates for Regression. Annals of Statistics, 15(2), 642-656.	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.
Tên gọi khác	Tukey bisquare M-estimator, Welsch M-estimator, redescending M-estimator, W-Tahmin Edici (Welsch / Tukey Bisquare)	MM-estimation, MM robust regression, high-breakdown high-efficiency estimator, MM-Tahmin Edici	S-estimation, robust S-regression, S-Tahmin Edici
Liên quan	4	5	5
Tóm tắt	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 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.	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.